by extension, rationals
#serious-discussion
tender tulip
rationals suck ass when solving for multivariate poly's
for example, x^3 + y^3 - 1 = 0 has no rational solutions
neat lintel
For me it was
\begin{align}
&(xy+yz+zx)^2\
&= xxyy + xyyz + xxyz + xyyz + yyzz + xyzz + xxyz + xyzz + xxzz\
%\intertext{this is the binomial formula}
&= xxyy + 2xyyz + 2xxyz + yyzz + 2xyzz + xxzz\
&= xx(-x-z)y + \cdots + yyz(-x-y) + \cdots + (-y-z)xzz\
&= -xxxy -xxyz + 2xyyz + 2xxyz -yyyz -xyyz + 2xyzz - xzzz - xyzz\
%\intertext{grouping terms}
&= -xxxy -yyyz -xzzz +xxyz + xyyz + xyzz\
&= -(x^3y+y^3z+z^3x) + (xyz)(x+y+z)
\end{align}
tender tulip
For me it was
it's not 9, I'll prove it by contradiction
fathom swallowBOT
Brudimann
tender tulip
Assume the aforementioned assumptions, then add |xy^3 + yz^3 + zx^3| = 9, then by our assumption, xyz is either -1/2 or 1/2
neat lintel
,rccw
fathom swallowBOT
tender tulip
guess it's -1/2, then we know that there is only one triple that works per 1/2 or -1/2
only ONE
tender tulip
the solutions to t^3 - 3t ± 1/2
tender tulip
you assume z = 0
neat lintel
You don't need to solve for roots, you don't need to introduce any new polynomials
tender tulip
adding an extra assumption and equality, allowing 3 equalities, and giving a unique solution
but without that third assumption, you cannot solve for a unique pair
tender tulip
Lets plot it on geogebra shal we
tender tulip
actually, these can all be considered projectively
neat lintel
And at the end
The answer is
neat lintel
It's 9
.
What do you mean projectively
All polynomials can be considered projectively lol
neat lintel
You mean homogenise
tender tulip
uNHO
neat lintel
tender tulip
I still don't agree with it being 9
neat lintel
You made a mistake
golden pendant
why if f is linear and f(x)<kx then f is continuous, intuitively
neat lintel
why if f is linear and f(x)<kx then f is continuous, intuitively
Lipschitz functions are continuous
tender tulip
why if f is linear and f(x)<kx then f is continuous, intuitively
isn't f being linear imply continuity
golden pendant
isn't f being linear imply continuity
on a finite dimension
neat lintel
Also that condition doesn't imply continuity
tender tulip
on a finite dimension
specify that then dippy
neat lintel
Consider dirac delta shifted to 1
tender tulip
you can't just throw an equality without some metric
neat lintel
:P
golden pendant
yeah
neat lintel
you can't just throw an equality without some metric
You can 
tender tulip
But we don't care about xyz
we d o
golden pendant
just, nvm
Is there somewhere i can train on true or false questions involving topology on normed vector spaces?
neat lintel
Yeah you read a book on NVS and ask yourself questions
golden pendant
Yeah you read a book on NVS and ask yourself questions
i did that
neat lintel
Ok
eager reef
why if f is linear and f(x)<kx then f is continuous, intuitively
did you mean functionals by this
then its true
nvm
neat lintel
do you guys have recommenedation any for resources on combinatorics
golden pendant
did you mean functionals by this
I was trying to understand it on the graph. What it means
tender tulip
you can show that xy^3 + yz^3 + zx^3 = 18xyz assuming the conditions we showed, then lets say 18xyz = 9, then (t-x)(t-y)(t-z) = t^3 - 3t - 1/2 {which we know exists}
golden pendant
for a norm of a function to be smaller than some k times x
to mean that its continuous
tender tulip
Which only gives 3 solutions to f(t) = (t-x)(t-y)(t-z), our roots,
golden pendant
if its linear
tender tulip
dipshits continuity
tender tulip
e x a c t l y
B U T xy^3 + yz^3 + zx^3 = 18xyz
so that must ALSO have infinitely many solutions
neat lintel
And why do we care about that equation
golden pendant
the function that takes x,y and give x+y is continuous for allllll norms?
my textbook just said, its continuous
didnt bother specify a topology
tender tulip
didnt bother specify a topology
on what vector space
golden pendant
balls generating something is tight
tender tulip
I guess any open set is the union of some collection of "balls" around points
neat lintel
I still don't agree with it being 9
Consider the equation whose roots are x, y, z :
(t−x)(t−y)(t−z)=0
This gives t^3 −3t=λ0, where λ=xyz. Since x, y, z are roots of this equation, we have
x^3-3x−λ=0, y^3−3y−λ=0, z^3−3z−λ=0
Multiplying the first by y, the second by z and the third by x, we obtain
x ^3 −3xy−λy=0
y ^3−3yz−λz=0
z^3−3zx−λx=0
Adding we obtain
x^3 y+y^3 z+z^3 x+z^3 x−3(xy+yz+zx)−λ(x+y+z)=0
This simplifies to
x^3 y+y^3 z+z^3 x=−9
(Here one may also solve for y and z in terms of x and substitute these values in x^3 y+y^3 z+z^3 x to get -9).
Not my way of solving this question, but this is one of the methods
tender tulip
I am still confused because my method showed that there is contradiction here
but I can't see an error
tender tulip
@vivid halo Hey bud, sorry for the ping, but I have a general question about elliptic curves again.
For L(x,y) = 4x^3 - ax + b - y^2, L(f(t),f'(t)) = 0 is parameterized over C via the Weierstrass elliptic function, and L(x,y) = 0 is genus 1, and has an addition formula from it's Jacobi variety by proxy of it's differential forms
BUT, for L(x,y) = (1-x^2)(1-mx^2) - y^2, L(f(t),f'(t)) is parameterized via the Jacobi Elliptic function sn. But L(x,y) = 0 is a genus 3 curve, but still has an addition formula, wtf is going on here.
vivid halo
I mean when you have a hyperelliptic curve y^2=f(x) where f(x) is degree 2g+1 or 2g+2
then this has genus g
tender tulip
huh
tender tulip
then this has genus g
Is there a way to "find" the addition formula on the power-torus for higher genuses
power torus just being the torus squared cubed or whatever
vivid halo
right so if you have a genus g curve X then associated to this is the Jacobian variety Jac(X) which is a complex torus of dimension g
tender tulip
what also bothers me is how the addition formula takes the form as an element of Q(a,b,c,d) so for any algebraicly closed field of characteristic 0 it should carry over
Idk if there is an addition formula for nonzero characteristic
vivid halo
by addition formula you mean the usual one for elliptic curves?
tender tulip
yes
I wonder if you can somehow define the jacobian variety outside of the specific case of the complex field
vivid halo
yeah I mean there are ways you can write down the addition formula over any ring
for fields of char 0 it's a bit simpler
yeah the Jacobian variety makes sense over very general rings
tender tulip
isn't it based on differential forms
I wonder if you can use the Zariski tangent or smth
vivid halo
the Abel-Jacobi map is usually defined this way, but there are other ways you can define this that make no reference to things over C
tender tulip
It'd like to see it
vivid halo
Jac(X) is the moduli space of degree 0 line bundles on X
tender tulip
I still don't understand the structure sheaf on the spectrum of a comm. ring though that much yet, besides what it is
or how its useful per say
vivid halo
you've seen the Nullstellensatz right?
tender tulip
you've seen the Nullstellensatz right?
yes.
vivid halo
right so that's for very special rings. The structure of Spec of a commutative ring is generalizing this Nullstellensatz to arbitrary commutative rings
vivid halo
well so here are a few phenomena that are captured by this that aren't captured by the kinds of rings you consider with the Nullstellensatz
tender tulip
Jac(X) is the moduli space of degree 0 line bundles on X
can this be done over any alg closed field?
vivid halo
can this be done over any alg closed field?
over any base scheme this should work
so this is very very general
tender tulip
wtf is a scheme
tender tulip
yeah
vivid halo
schemes are more general than varieties in exactly the same way that Spec(R) is more general than MaxSpec(R) where R is the kind of ring that the Nullstellensatz applies to
tender tulip
huh
I mean I still don't really find the structure sheaf motivating, but I also barely understand it
vivid halo
one of these ways in which they are more general is nilpotents. A good example is Spec(C[x]/(x^2)), as a variety this is just a single point but as a scheme this has like, some infinitesimal direction
you think of it as a point plus a tangent vector
this is reasonable since maps Spec(C[x]/(x^2))->X into a complex variety X are exactly points of X plus a tangent vector at that point
this sort of infinitesimal direction stuff is something that is only captured by schemes rather than varieties
the other thing that schemes do for you is you don't have to work over algebraically closed things anymore
tender tulip
Isn't the ring for any open set K in the zariski topology the limit of the localizations by every element in the open set or smth
I have the def written down, I barely understand it aside from it inducing a sheaf
vivid halo
I mean the easy way to remember the structure sheaf for Spec(R) is it's given by localizations R_f on the distinguished opens D_f
and then for general opens yeah you have to write down some limit in general
tender tulip
Let I be the intersections of all ideals containing element x, then D_f is Spec(R)\V(I) right
vivid halo
mhm
tender tulip
alright
i haven't considered the limit in the category of comm rings yet, shit
is there an alternative def
Yo what if
I have a stupid idea
vivid halo
I mean this is the definition and you get used to computing with it 
I think this is just one of those definitions you have to think carefully about in some specific examples, like R=Z, k[x], Z[x], etc
tender tulip
If we have some comm semigroup S, we can define a subset of S, K, to be an ideal iff xK = K for all x in S. Then we can define L(S) to be the set of all ideals, and we can say a prime ideal P is an ideal such that for all x and y in S, xy in P <=> x in P or y in P. AND THEN we can define the spectrum of this semigroup, and define the zariski topology similarly and sheaf similarly
tender tulip
i wonder if it will still be a sheaf
vivid halo
anyways however you believe this definition of Spec(R) with its structure sheaf
you need this structure sheaf to glue these together
schemes are spaces with a structure sheaf that are glued together from various Spec(R)'s and their structure sheaves
tender tulip
This is my first interaction with a sheaf
tender tulip
schemes are spaces with a structure sheaf that are glued together from various S...
aah
but why do we consider locality and the limit to define the sheaf
vivid halo
I mean the whole point of the definition of sheaves is to make sense of locality and gluing
tender tulip
From one ideal I, we can get an open set in the Zariski topology from considering the prime ideals not containing I, but also a ring by considering the limit of localizations by powers of each of it's elements which still doesn't feel motivating
besides that sheaf conditions follow
vivid halo
yeah admittedly the definition feels a little unmotivated in this example
tender tulip
I can sorta see why limits are used cuz it's univ property
Also i think R_x is iso to R[X]/<1-Xx> i think
neat lintel
the function that takes x,y and give x+y is continuous for allllll norms?
Triangle inequality
vivid halo
somehow once you fix the open sets of the Zariski topology, and you fix the idea that O(Spec(R))=R and this should be compatible with the open subsets in the sense of being local
then probably this forces the localization definition on you
tender tulip
localization probably just generalizes nullstellensatz in the specific variety example
vivid halo
well right that's the other point, if you do this for R=C[X_1,...,X_n] and you look at what's happening at the maximal ideals
if you want this to be compatible with Nullstellensatz then you have to use localization
tender tulip
yeah
neat lintel
N
vivid halo
the really crucial point is that the stalks of this structure sheaf are local rings
so Spec(R) with its structure sheaf is a so called locally ringed space
this is the crucial thing that is needed when gluing schemes
tender tulip
the localization of R/P is local afaik
I forget what the maximal ideal is though
someone used a tensor product which I avoid
I don't want to use tensor products, I don't understand them
vivid halo
you should get comfortable with tensor products 🙂
tender tulip
They feel really confusing for the specific examples of rings
I tried and failed constructing them
vivid halo
oh yeah there are some examples that are a huge pain to actually work out explicitly
you know the categorical properties though, yeah?
tender tulip
not really
vivid halo
oh well here's something you'll like
If you have ring maps A<-R->B
then the tensor product A\otimes_RB is the pushout of this diagram
tender tulip
also those morphisms are mono right
vivid halo
$\begin{tikzcd} R \arrow[r] \arrow[d] & A \arrow[d]\ B \arrow[r] & A\otimes_RB \end{tikzcd}$
fathom swallowBOT
nGroupoid
vivid halo
they don't have to be mono
tender tulip
it's the colimit of this diagram
I'm still not following very well
vivid halo
this means whatever the universal property of colimits means
vivid halo
$\begin{tikzcd} R \arrow[r] \arrow[d] & A \arrow[d] \arrow[ddr]\ B \arrow[r] \arrow[drr] & A\otimes_RB \arrow[dr,dashed]\ & & Z \end{tikzcd}$
fathom swallowBOT
nGroupoid
vivid halo
if you have a commutative square involving R, A, B, Z then you get a unique map from the tensor product
tender tulip
hm
vivid halo
(btw Spec turns this pushout diagram into a pullback diagram)
vivid halo
what, constructing the tensor product from universal property?
tender tulip
yes, or how can we construct the tensor product give the quintuple (R,A,B,f_a,f_b)
Just subring A x B of pairs (a,b) such that f_a(a) = f_b(b) ?
vivid halo
well so the maps R->A and R->B make A and B into R-algebras, so they can be regarded as R-modules and you can take their tensor product A\otimes_RB as an R-module
tender tulip
I don't understand tensor products of modules either aaaaaaa
vivid halo
This R-module A\otimes_RB you don't want to regard as a sub of AxB
right so let's understand this
you do have a map of R-modules AxB->A\otimes_RB
tender tulip
alright
vivid halo
so this sends a pair (a,b) to the tensor a\otimes b
then this satisfies some universal property: if you have an R-bilinear map f:AxB->M then this corresponds uniquely to an R-linear map f':A\otimes_RB->M
i.e. you get the obvious commutative diagram with the map AxB->A\otimes_RB
vivid halo
well right we haven't written something explicit like "the tensor product is the set of blah blah such that blah blah"
and that's kind of hard to do in general
tender tulip
yeah it just feels unmotivated and confusing otherwise
like what "IS" the tensor a x b
vivid halo
well right we can name the element a\otimes b, it's the image of (a,b) under this canonical morphism
we can say some obvious relations that this satisfies, from what was said about (bi)linear maps
so you have relations like a\otimes(b+b')=(a\otimes b)+(a\otimes b') and so on
tender tulip
I wish you could just quotient A x B in some way and be like "it's the class of pairs..."
vivid halo
every element of A\otimes_RB can be written, non-uniquely, as \sum_i a_i\otimes b_i
the issue is the non-uniquely part
meager sonnet
you can in vector spaces but its generally less informative than the universal property
vivid halo
every element of A\otimes_RB can be written, non-uniquely, as \sum_i a_i\otimes ...
unfortunately there isn't a more explicit description than this, and if you want a really explicit description you have to worry about individual examples
but okay this is still something: we know how to write elements, we know some basic relations they satisfy, we know the universal properties that everything satisfies
that's a good starting point at least
tender tulip
Can we somehow quotient out the coproduct
vivid halo
sure you can write the tensor product as a quotient
like the quotient is just us imposing the various relations on AxB
tender tulip
yeah
vivid halo
this should work in general, no?
tender tulip
but overall I don't see why we need the tensor product for the sheaf discussion
eager reef
my mind went to free because of the way its constructed as a quotient of the free module generated by the module itself
i think
vivid halo
but overall I don't see why we need the tensor product for the sheaf discussion
I mean this isn't related to sheaves, although if we are talking about Spec(R) this ends up being a very important construction
tender tulip
I mean this isn't related to sheaves, although if we are talking about Spec(R) t...
What is the maximal ideal of A_(R/P) where P is a prime ideal tho
oh
Probably all a/b, a in P, b not
I wonder if there's another way to construct A_(R/P) where P is a prime ideal
anyway back to elliptic curves
If I was just given the definition of an elliptic curve over a field, can I still derive the addition formula
vivid halo
right, back to the topic at hand
right so there is a very general point addition formula you can derive
tender tulip
how would I actually "find" it
vivid halo
so I mean the usual addition formula should work fine, yeah?
there are some issues in char 2 and 3
but ignoring those
tender tulip
actually in general, for what varieties can there be an addition formula
without referencing complex numbers
for genus via R-R
and for those varieties, how would you find it
vivid halo
so if you have a projective algebraic variety that is also an algebraic group this is extremely restrictive: this implies the group is automatically commutative, and these are Abelian varieties
in the curves case these are elliptic curves and then in higher dimensions these are still all tori
for non-projective varieties there are a lot more possibilities, now you're basically just asking about classifying algebraic groups
vivid halo
so the nice way to think about the addition formula on elliptic curves that works nicely over any base ring is to realize the elliptic curve is its own Jacobian variety
the Jacobian variety parameterizes degree 0 line bundles on the elliptic curve, and the addition formula is just given by tensor product of line bundles
the unit object is the structure sheaf
tender tulip
So what you're saying is, a projective variety has an addition formula (abel variety), then it's a projective surface & an elliptic curve to be specific
vivid halo
that's if your projective variety has dimension 1
then yes if you have a group structure that group structure has to be commutative and your curve is an elliptic curve
tender tulip
what about dim 2 and higher
vivid halo
in higher dimensions you're talking about Abelian varieties
for instance in dimension 2 you're talking about Abelian surfaces, so these are either Jacobian varieties of genus 2 curves, or a product of 2 elliptic curves
tender tulip
ok
vivid halo
in really high dimensions not every Abelian variety can be written as a Jacobian variety like this, but whatever
they are still like higher dimensional analogues of elliptic curves in the way you expect: over C they are complex tori of the form C^g/L for some lattice L
tender tulip
the Jacobian variety parameterizes degree 0 line bundles on the elliptic curve, ...
i still don't know what line bundles are either that much
vivid halo
well so the structure sheaf is a line bundle (it's the trivial line bundle)
in general line bundles locally look like this
tender tulip
okay
vivid halo
so you can find some open cover such that the restriction to each open is the structure sheaf on that open
so globally it might be twisted in some interesting way but locally it's trivial
tender tulip
h jacobian variety is really complicated lol
vivid halo
yeah
but yeah if you're doing explicit coordinate computations of the group operation
tender tulip
yea
vivid halo
then the usual formula should work, as long as you're not dividing by the characteristic of your field
tender tulip
For the current situation I'm mostly considering the simplest examples of varieties
the variety coming from a specified-number-variable ring quotiented by a specified prime ideal
I started with wondering why the fuck the elliptic curve has a fucking group structure anyway which seems really random
turns out there's a lot more to it ig
vivid halo
yeah it is quite special
tender tulip
yeah it is quite special
it seems really specific
vivid halo
I do think the Jacobian explanation of this is the most clarifying
the usual thing involving like
tender tulip
And the jacobian variety is also complicated as fuck
tender tulip
secant lines or whatever
provides no insight into the associativity
tender tulip
IS there like a "simple way" to construct the jacobian variety
vivid halo
another nice way to write it is in terms of divisors
tender tulip
Line bundles confuse me but there probably isn't a simple way
vivid halo
divisors on curves are simple things, they are formal Z-linear combinations of points on the curve
tender tulip
are they more annoying on surfaces
vivid halo
yeah, in general divisors are Z-linear combinations of irreducible codimension 1 subvarieties
on curves codimension 1 subvarieties are just points and those are easier to parameterize
tender tulip
divisors on curves are simple things, they are formal Z-linear combinations of p...
principal ones are like, ones corresponding to regular funcs right
vivid halo
right exactly
tender tulip
or smth
vivid halo
so the Jacobian variety here, as a group, is degree 0 divisors modulo principal divisors
tender tulip
I wanted to look into regular functions because I remember nullstellensatz causing some neat isomorphism i can't remember explicitly
something with the localization
The paper's printed in my stack of papers on my desk I don't want to look through rn
i don't remember
vivid halo
there is a nice correspondence between line bundles and divisors that's like
tender tulip
something with the localization
Oh yeah, poly ring
vivid halo
a divisor D corresponds to a line bundle O_X(D)
tender tulip
OOHHH, I just remembered why I learned localizations lmao
vivid halo
the sections of O_X(D) are functions with zeros and poles given by the divisor D
on your elliptic curve you have a nice supply of degree 0 divisors, namely differences of points [p]-[q] for p and q points on the elliptic curve
tender tulip
huh
vivid halo
this has a corresponding line bundle O_E([p]-[q]) of degree 0
when you work out the addition formula given by tensor product of line bundles
the "usual" secant line formulation falls out of this more or less
tender tulip
OOHHH, I just remembered why I learned localizations lmao
For some algebraicly closed field K and element x, I wanted to consider K_(x,n), n in Z, which is the ring of rational functions where at x the pole/zero has degree n
which didn't work out for reasons
but I fixed what I was asking for and got one
vivid halo
right, but this sounds somewhat close to these line bundles O_X(D)
tender tulip
right, but this sounds somewhat close to these line bundles O_X(D)
huh
my definition broke down because I didn't really know what I was looking for
I wanted to define some algebraic structure on the set of rational functions F(x) such that at some element a, the pole has order n
but that doesn't work lol
T U R N S O UT
i'm dumb
AHA!
I also need to disconnect varieties from ideals
You can map ideals to varieties, and varieties to ideals, but composing them gives the ideal's radical by nullstellensatz
@vivid halo I've always defined an affine variety by saying that they're the vanishing set of a prime ideal of a poly ring, but can you like, can you construct them some other way
vivid halo
right so you could define these as like, Spec(k[x_1,...,x_n]/(f_1,...,f_m)) where (f_1,...,f_m) is some prime ideal in k[x_1,...,x_n], but this is just equivalent to what you said
tender tulip
ye
We can map sets of polys to sets of tuples via affine algebraic sets ig
I wonder if for sets of polynomials A and B, if V(AB) = V(A) union V(B)
probably not
vivid halo
well how are you defining the product AB here
tender tulip
any sum of pairs ab, a in A, b in B
vivid halo
then that definitely can't be true by counting the number of components, right?
tender tulip
yeah, true
vivid halo
it is true if A and B are singletons lol
tender tulip
fa ir
dry leaf
is it ok to be an average student? 70's?
Ive been average all my life even outside school play video games ride my book and work my job at the hospital but is that a bad mindset?
lavish kayak
Define bad
lavish kayak
whats so bad about that?
Nothing
It's realistic and healthy
Why do you need us to validate you?
dry leaf
because
i dont see much of average students talking
its mostly top students with 90's+
u never hear the middle ground
dry leaf
why
dry leaf
am I lying to myself then being a average student or am I just lazy and dont wanna work hard who knows but these are my marks would u show them to your parents or no? https://i.imgur.com/R2s9LhK.png
if u were a teacher
what would u think
im not getting 10's does that mean im missing 30% of my knowledge?
dry night
The people who talk here are simply people passionate enough to actively discuss math
It doesn't necessarily have to do with grades
I'm more or less the same in grades with you
dry leaf
its so depressing i feel like im in the cracks the top students always get attention
then bottom students who fail dont even care
middle students i feel lost lol
its like can i do better but im still ok with 75%...
dry night
Personally, I don't care much for other opinions
dry leaf
if im average will i do okay in life?
all the good jobs dont they go to high 90's+ students?
dry night
And I don't see grading percentage as a metric for how much knowldge I have
dry leaf
what are u in school for college? or still highschool
dry night
I'm in Uni
dry leaf
taking what
dry night
Studying Electrical engineering with a minor in applied physics
dry leaf
but ur smarter than me tho
im taking college at a community college
ur degree>whatever I get
even if u sit with 60's lol ur degree out weighs my community college
dry night
What are you studying
Also, you seem to conflate the prestige of your college with how smart you are
dry leaf
im in school to become a Licensed practical nurse (one step lower than nurse)
u can take it a community college
but if u wanna upgrade to Rgistered nurse u can bridge --->university
dry night
Are you looking to do that?
dry leaf
i was taking plumbing but hate it
yes right now im taking prep chem/prep biology to help my marks then to uni for me lol
dry night
I'm not aware of what it takes to be a registered nurse so you mihgt have to give me a few details
dry leaf
well theres 2 levels of nursing
LPN=licensed practical nursing and RN=Registerd nursing
once is at college and the other uni
once starts 33 to 30 the other is 45
idk if that makes sense lol
dry night
Are you looking to be registered?
The best I can give you here is simply that if you find it worth it to chase after loftier goals, by all means do it, even if it means to put in even more hours of study and work
Some of the smartest people you meet aren't people of natural talent but sheer work ethic and discipline
river moon
im not getting 10's does that mean im missing 30% of my knowledge?
grades aren't knowledge
I personally don't care if I barely pass my microeconomics or law classes this year because I'm a CS student and I hate both economics and law and I'm never going to work in these fields
neat lintel
LPN=licensed practical nursing and RN=Registerd nursing
What about cRNA?
Is that a proper subset of RN?
dry leaf
im already a healthcare aide upgrading to LPN
wait
CRNA
Is a CRNA a doctor?
An anesthesiologist has a Doctor of Medicine (MD) or Doctor of Osteopathic Medicine (DO) degree, whereas a CRNA is a registered nurse who has a doctoral-level degree and has passed the National Certification Examination for Nurse Anesthetists.Mar 17, 2022
idk
languid comet
>Is a CRNA a doctor?
An anesthesiologist has a Doctor of Medicine (MD) or Doctor...
Techinically no
They have different paths
languid comet
Both administer anesthesia but in terms of respect anesthesiologists are better
languid comet
https://www.youtube.com/watch?v=vBSWbFis5YY
What’s rhat
dry leaf
LPN Licensed pratical nurse
languid comet
Registered nurse?
languid comet
So just a bachelors?
languid comet
You wanna be a nurse?
dry leaf
its just a way for the goverment to cut costs and pay people less lol
I want to be a nurse in either corrections or the airforce
on a aircraft carrier
or a submarine
languid comet
its just a way for the goverment to cut costs and pay people less lol
Nice
languid comet
Oh so like a rn?
dry leaf
WHICH is why most go upgrade to RN
yes
they become a LPN for a few years then go back to school
and upgrade their pay
languid comet
So the military is a ticket for less time?
dry leaf
because as a LPN I have jobs everywhere?
hidden phoenix
but when the woman walks back wouldnt it violate one of the rules as the other husbands are in the presence of another woman that is not with her husband
languid comet
because as a LPN I have jobs everywhere?
Oh yeah but it’s sorta not traditional
languid comet
im also a pretty boring person..
Haha dw
languid comet
i kinda wanna see other parts of the world
Yeah
dry leaf
btw
this is MY program im taking
AND
this is UNI Level
if u dont got the marks you take what im taking at community college practical nursing (LPN) THEN bridge to university level and become a full regisistered nurse(RN)
thats what some people do that have 75% lol
since to get into uni u need like 90%+ lol
languid comet
since to get into uni u need like 90%+ lol
90 percent marks?
languid comet
Oof
dry leaf
but for me im okay at the college level im totally ok with 30 to 35 an hour
languid comet
Is the specific department for uni nursing maxed out?
languid comet
but for me im okay at the college level im totally ok with 30 to 35 an hour
It’s not bad tbh
During college try to get job experience
Looks more appealing
dry leaf
btw idk where u live but
in canada
college=community college
uni=university
just so u wernt confused
i mean
atleast in toronto thats how it is......
hearty marten
umbral lion
atleast in toronto thats how it is......
its that way for most of the country dw
but are you fr?? 90+ for fucking NURSING??
i remember back when i was applying i thought it was excessive to have a top6 that was 80+ for most nursing programs
not that iwas going into nursing but i knew a few folks who were
dry leaf
take note the bottom route
thats whati m doing
@umbral lion @languid comet
because of the buget x they can hire only so mcuh a hire
they have to get the best means stiff school requirements for uni
umbral lion
fuck im so sorry homie leave this place if you can lmao
i knew someone who had an easier time getting into a law program in europe rather than doing pre law here
dry leaf
oh im just gonna be a Registered practical nurse
no uni lol
im perfectly okay with 35 an hour lol
and 16month course
does taking prep courses to get me into the program
the college leve one now 👍🏿
flint thunder
There are some good things about Ontario. For example you all have mostly renewable power (hydro)
umbral lion
that does nothing for the average person
if anything it raises the already sky high energy bills
dry leaf
yeah that dosent help me lol
umbral lion
ontario is the sorta "hell"scape where only the rich and the immigrated have a good itme
flint thunder
if anything it raises the already sky high energy bills
What? Long-term it is very good, you are independent of fossil fuels
umbral lion
long term nobody will live here
flint thunder
ontario is the sorta "hell"scape where only the rich and the immigrated have a g...
Also everyone has health insurance, right?
umbral lion
its not useful health insurance if it takes you upwards a year to get treatment for life threatening things
flint thunder
its not useful health insurance if it takes you upwards a year to get treatment ...
Right, but here in the U.S. if you go to the emergency room you can be literally bankrupted
umbral lion
i have a buddy who's hand is nearly forfeit due to poor surgery and being scheduled for another year down the road to fix it
umbral lion
Right, but here in the U.S. if you go to the emergency room you can be literally...
would you rather be bankrupt or out of a hand?
flint thunder
would you rather be bankrupt or out of a hand?
I have no idea the details of the situation there honestly
umbral lion
that is the whole deal
either you lose your hand
or you be bankrupt
WHICH DO YOU CHOOSE?
flint thunder
I guess bankrupt? You don't have emergency rooms there?
umbral lion
the emergency rooms are a bit of a coin toss
flint thunder
OK.
umbral lion
sometimes you get treatment a few months ahead, or you get bumped up the line, or you get left worse off and the government hounds you
flint thunder
I am not trying to tell you your life there is perfect or anything, I was just pointing out that there are some advantages
umbral lion
your "advantages" are definitely being preached to the wrong audience
getting all uppity about environmentalism while people can't afford to eat is a bit poor in taste you know?
flint thunder
Uppity? There are many people who cannot afford stuff in EU because it's all fossil fuel based, people in Ontario are quite lucky to be saved those costs
umbral lion
care to explain?
dry leaf
would you rather be bankrupt or out of a hand?
bank rupt
💯
lol
theres just no question 
umbral lion
good to know in my sample size of 2
flint thunder
care to explain?
There isn't much explanation required. Hydro is one of the cheapest forms of electricity and is renewable, so you don't have to import it from Russia or whatever.
umbral lion
we all agree
dry leaf
also as a canadian i wouldnt mind private healthcare here and there mixed in with public
it would be less wait times
umbral lion
There isn't much explanation required. Hydro is one of the cheapest forms of ele...
That doesn't really correlate with what stuff is not left affordable, also isn't it the EU's corruption problem that lead them back into fossil fuels?
which is definitely something ontario has had in spades
so i think we're all in the same shitberry float
umbral lion
nothing positive lel
umbral lion
shore
azure nymph
Well the problem with bankruptcy is in America at least it makes it extremely difficult to do pretty much anything, wanna buy a house or even rent good luck, car good luck unless you're paying cash, open new accounts pffft, assets seized, insurance premiums will go up. So yeah while you can see a doctor who really doesn't have to give a shit about you and can discharge you if they can reasonably claim to not believe your is serious enough, it's not exactly as easy as it sounds.
flint thunder
Well the problem with bankruptcy is in America at least it makes it extremely di...
It's difficult to explain this kind of stuff to people who aren't in the U.S. because I don't think people in most countries have experienced these kinds of things
Europeans are usually horrified to find out about these situations
azure nymph
God forbid they prescribe you anything cause you won't be getting that
ripe wasp
hey i’m doing the exact same thing in my chem class
it wasn’t that difficult tbh
nomenclature is really cool imo
it’s fun
kinda feels like math
neat lintel
is there a word for subperfect?
like if im making a burger and i choose the tastiest meat the tastiest bun the tastiest sauce
that would not necessarily make it the tastiest burger
but a good burger overall
is there a word for it
mint canopy
is there a word for it
Dunno about the mathematical concept (this is too vague for that I think) but this is related to the fallacy of composition, wherein one assumes that if every component of something has a property, then so must the whole.
dry night
Sounds similar to the concept of Gestaltian psychology, but I don't know if there is a strict word for this that I know of
neat frost
Ryc
deep mango
This morning I had crepes and I was faced with a decision
neat frost
I love you and I love crepes
neat lintel
where do you even buy crepes
neat frost
You better have taken a picture you scallywag
proven hornet
nutella crepes are good
deep mango
I made them
gaunt latch
lmao
neat lintel
ryc, are you my mom?
neat frost
No y’all go away this is my convo with ryc
deep mango
i actually made them with my mom too
neat frost
Ryc. Did. You. Take. PICTURES
deep mango
No, I didn't
flat harbor
crepes are cool but i want a chicken waffle so bad rn
deep mango
Anyway I was faced with a dilemma
neat lintel
Crepes don't deserve to be as tasty as they are with such little effort
proven hornet
crepe origami
deep mango
they can be folded twice, to make a quarter
neat frost
they can be rolled
No that makes them a blintz silly billy
neat frost
they can be folded twice, to make a quarter
This is the correct method
deep mango
you can even do a foldover inside to make thirds
flat harbor
taco vs burrito vs quesadilla....
neat frost
Nono quarter
flat harbor
make a crepe burrito
deep mango
This is the correct method
i usually do this and i like it the best but this presents further decisions
for example
neat frost
make a crepe burrito
THATS A BLINTZ
sacred forge
taco vs burrito vs quesadilla....
döner
deep mango
do the fillings occupy 2 pockets or just 1?
umbral lion
you can even do a foldover inside to make thirds
wouldnt it be an eighth?
neat frost
do the fillings occupy 2 pockets or just 1?
You have the crepe flat. You smother it with filling. then you fold
flat harbor
THATS A BLINTZ
again with the "blintz"... u euromericans get wilder each day
neat frost
How many pockets that covers idk
neat frost
again with the "blintz"... u euromericans get wilder each day
I’m neither European nor American you silly goose
flat harbor
practically both given geopolitical and historical reasons
sacred forge
europeans and americans can not be grouped
neat frost
practically both given geopolitical and historical reasons
True but fuck you
flat harbor
westerner doesnt have the same ring to it
neat frost
Geographically I am neither
deep mango
wouldnt it be an eighth?
uhh the way im thinking of it involves a little flap that you create to get thirds
idk
deep mango
You have the crepe flat. You smother it with filling. *then* you fold
smother?
neat frost
Yes
gaunt latch
Slurp is asian
neat frost
Like when someone is lying down
deep mango
my crepes include chocolate chips, banana slices, and strawberry slices
neat frost
And you smother them with a pillow
deep mango
nothing is smothered
neat frost
Smother
neat frost
my crepes include chocolate chips, banana slices, and strawberry slices
Where’s the SPREAD
The Nutella??
proven hornet
banana pancakes 😋
deep mango
nutella?
umbral lion
uhh the way im thinking of it involves a little flap that you create to get thir...
okay i see now i think
deep mango
nutella is fucking rank
neat frost
Hell I’d even let you off with some jam
neat frost
nutella is fucking rank
Fuck you shitface
sacred forge
westerner doesnt have the same ring to it
post-renaissance people
flat harbor
nutella is fucking rank
cunt
deep mango
nutella is literally disgusting
neat frost
Chocolate chips???
proven hornet
no
gaunt latch
so traditional
umbral lion
Fuck you shitface
canadian nutella is foul tbh
neat frost
Are you fucking INSANE???
flat harbor
nutella is literally disgusting
cunt
proven hornet
Nutella is fantastic
deep mango
remember when i was a kid and was like "wow nutella is so yummy! i love chocolate"
lol
neat frost
Chocolate chips are tenth rank (not second rank, not third rank, etc) chocolate
Literal CRAP
sacred forge
mint chocolate and orange chocolate are both disgusting
umbral lion
they make nutella differently depending the country you're in and in canada its shiny and very oily
flat harbor
too edgy for nutella....
neat frost
You should’ve taken ACTUAL chocolate and melted it
flat harbor
hes gone senile
deep mango
if i wanted nut spread i would use almond butter or something
velvet dagger
I'm sorry this is contrarian even for you
gaunt latch
who thinks that nutella is an actual chocolate thing
fading tusk
my crepes include sugar and contreau
proven hornet
mint chocolate and orange chocolate are both disgusting
Orange chocolate is damn good
deep mango
hazelnuts are a bad nut
neat frost
Nutella is about BOTH the hazelnut and the chocolate
neat frost
hazelnuts are a bad nut
Cunt.
umbral lion
poor ryc
deep mango
and nutella is only popular because it's semi-chocolatey
flat harbor
some opinions are just wrong
sacred forge
Orange chocolate is damn good
horrible
velvet dagger
The point is the mix
deep mango
but who am i trying to impress? i'll just eat chocolate
neat frost
Ryc did you even melt the chocolate chips?
flat harbor
i take it back ure not entitled to ur own opinions
sacred forge
chocolate should never be combined with fruits, ever
deep mango
Ryc did you even melt the chocolate chips?
the crepe was hot so they half melted
neat frost
And why didn’t you use ACTUAL chocolate instead? (Like a chocolate bar)
deep mango
but i like there to be some of that chalky chocolate texture still there
proven hornet
Get some cookie butter from trader joes 
gaunt latch
hazelnuts are nuts not fruits
neat frost
the crepe was hot so they half melted
Okay yeah that’s the way to go
velvet dagger
That specific hazelnut + chocolate mix is better than most chocolate with or without nuts, and basically any non-chocolate nut
neat frost
Tho they should be more melted than half
sacred forge
fruit ruins chocolate, and chocolate ruins fruit
deep mango
no way dami
neat frost
Also good morning dami!
deep mango
i just don't think hazelnuts are good
flat harbor
Tho they should be more melted than half
i like the crunch
proven hornet
fruit ruins chocolate, and chocolate ruins fruit
So you don't like chocolate covered strawberries?
gaunt latch
NUTS WITH HONEY IS THE BEST
velvet dagger
I mean some people think the earth is flat
neat frost
Tbh recently I’ve learned that every other mod is both cooler, chiller, and more sane than ryc
velvet dagger
🤷
sacred forge
So you don't like chocolate covered strawberries?
i hate them, the strawberry on its own is way better
proven hornet
the earth can be any shape you like 🙂
sacred forge
its a lose lose situation
flat harbor
every mod is well adjusted and u talk to them and theyre just normal ppl
fading tusk
if u take the integral over the entire month good food does 0
gaunt latch
honey > chocolate 😔
flat harbor
then u have ryc whos too hipster for nutella
velvet dagger
Tbh I'm not much of a nuts person in general aside from hazelnut when it's nutella, and peanut butter lmfao
neat frost
Tbh it’s surprising that ryc doesn’t like nuts…
sacred forge
hazelnuts are amazing especially if they're roasted, pistachios are even better
velvet dagger
I get the appeal for sure but it's not me
Doing good slurp, feels good to live in the land of good takes. How about you?
How about you?
gaunt latch
Dami.. what type of nuts are you talking about?
umbral lion
dami is offbthe insanity pills again
flat harbor
nutella isnt even a condiment meant to be savoured for its rich flavours
sacred forge
Tbh I'm not much of a nuts person in general aside from hazelnut when it's nutel...
what about pistachios?
velvet dagger
Idk about types of nuts lol
neat frost
I’m doing swell. It’s a nice change for people to attack ryc for his shit takes rather than me
flat harbor
its a chocolatey spread u put into cheap meals to feel good abt urself for half an hr or so
gaunt latch
Idk about types of nuts lol
the one I am talking about is a lot of nut types inside a honey jar :))
flat harbor
now heres a real doozy
umbral lion
its a chocolatey spread u put into cheap meals to feel good abt urself for half ...
instantly vomitting afterwards to preserve your figure
flat harbor
i love vegemite
neat frost
How about you?
Also you asked this twice
velvet dagger
How abouty ou?
flat harbor
more ppl shuld try vegemite and try it enough times to the point they grow fond of it
neat frost
i love vegemite
Fuck off blo
neat frost
How abouty ou?
I’m doing swell. It’s a nice change for people to attack ryc for his shit takes rather than me
velvet dagger
blo idk what vegemite is but
gaunt latch
Dami.. this honey jar costs like 60$ 😔
flat harbor
its a NATIONAL CLASSIC slurp an entire nation cant be wrong
neat frost
Vegemite is Aussie marmite
sacred forge
vegemite is actually pretty good
velvet dagger
If you have to try something "enough times to the point they grow fond of it"
neat frost
I think it’s like vegetable paste
velvet dagger
That's called Stockholm syndrome
flat harbor
its a very salty marmite
neat frost
All you need to know is that it’s a dark brown color and it’s not chocolate
flat harbor
That's called Stockholm syndrome
if the entire world had stockholm syndrome wed call it growth pains
velvet dagger
Some would I'd just call it what it is tbh
sacred forge
can we appreciate pistachios please
sacred forge
nooo
velvet dagger
Pistachios are in the zone of, I get the appeal but I don't really go for them
If you get what I mean
gaunt latch
can we just eat without fighting over that
flat harbor
pistachio is like if u give me some i guess ill finish it
flat harbor
can we just eat without fighting over that
wheres the fun in that
gaunt latch
should I fight over nuts?
flat harbor
shuldnt u?
velvet dagger
I mean in fairness, nuts in general aren't like, the highest tiers of food to really be fighting over
gaunt latch
okay blo.. I'd steal your nuts at the end of the fight
sacred forge
the nut wars
velvet dagger
Pizza on the other hand... I'd def be willing to throw hands over people's pizza opinions
flat harbor
well yea but then it always ends up with like
sacred forge
I mean in fairness, nuts in general aren't like, the highest tiers of food to re...
strongly disagree, they are S class food
velvet dagger
Blo are you from Australia?
flat harbor
why are there so many cheese fans here
velvet dagger
I ask because of the vegemite mostly
sacred forge
agree cheese all basically tastes the same
flat harbor
Blo are you from Australia?
i lived there for 6 yrs
sacred forge
cheese is good as a complement, but its kinda overrated
velvet dagger
Wait in general the notion that all cheese tastes the same is very incorrect
gaunt latch
agree cheese all basically tastes the same
no lmao
flat harbor
i love cheese
gaunt latch
you guys didn't try enough types of cheese
flat harbor
but they all just taste the same i cant tell the difference
flat harbor
like i can feel difference in texture
gaunt latch
there are a lot of types
flat harbor
and cream cheese or feta is obviously different
but mozzarella, american, swiss and cheddar all taste the same to me
sacred forge
my favorite cheeses are goat cheeses, i like the acidity of them
flat harbor
give or take a bit of saltiness in cheddar?
gaunt latch
literally i tried over 550 types of cheese over my life
velvet dagger
Swiss cheese is less salty than cheddar yeah
gaunt latch
no one here is a cheese fan like me
velvet dagger
A sense in the mouth that isn't texture hmm I wonder what that's called
flat harbor
SILENCE
gaunt latch
there's like over 1,700 different types of cheese in the world
I am about to taste them all
sacred forge
aroma?
flat harbor
smth like that i guess
flat harbor
i can feel that stuff if i tried i guess
but if u made me close my eyes and eat some cheese
itd be like telling pepsi and coke apart
velvet dagger
Well
flat harbor
i just cant
velvet dagger
Okay so here's the thing about coke vs pepsi
sacred forge
pepsi is better than coke from what i can tell
velvet dagger
With each there's actually enough variation that there's no one thing you can call coke and one thing pepsi
flat harbor
yea! and thats how i feel abt cheese
like i cant sense a consistent "cheese taste"
that isnt common for all cheese
sacred forge
and lemon colas, whether its coke or Pepsi. are highly underrated
velvet dagger
I mean again look at brie vs cheddar vs swiss for instance
That + American + cream cheese are prob the most common ones for me?
flat harbor
the cheese that i can probs find if i go to the super
are mozzarella, american, cream and maybe some wheels of swids
ive tried cheese platters where theres a variety of cheese tho
maybe the platter was just a shit platter
opal bison
sacred forge
i see cheese more as a seasoning than food
flat harbor
i also like munching on cheese and drinking wine
but in those cases i think its always the kind of cheese that has stuff with it
sacred forge
oh youre one of those cheese snobs
flat harbor
nah i dont mind american cheese with wine
im telling u i cant tell the difference lmao
sacred forge
lol
flat harbor
just mold it into cubes and id be none the wiser
sacred forge
like i can tell the difference, but they don't have a difference in the grand scheme of things
flat harbor
i dont think many things do
sacred forge
spaghetti isn't as good without cheese
so in that case i love cheese
but not on its own
flat harbor
i think most meals can be improved with cheese
anything spicy, anything dry, anything saucy
flat harbor
salad cheese is good tho
sacred forge
nah, if youre going to eat a salad, dont half ass it
flat harbor
i like how it doesnt taste like much but it still tastes like cheese
i dont get ppl who just pour dressing over cabbage and call it a salad yea
at least put some olives and onions in there fam
sacred forge
i was very disappointed when someone put feta cheese in my döner i was very very disappointed
flat harbor
at midnight???
sacred forge
ye i know one place that is open at midnight
gaunt latch
so fuckin fresh
it is the most fresh juice ever
i love that
it slows my heart beats
sacred forge
redbull is probably the best tasting drink
but i dont drink it that often
because its bad for you
gaunt latch
have you tried cold roselle
flat harbor
redbull tastes alright
fair mural
but it gives you wings
flat harbor
saying that it tastes the best is a strongass statement
sacred forge
never had roselle
gaunt latch
roselle tastes better than redbull
it is just the most fresh thing you can ever drink
sacred forge
saying that it tastes the best is a strongass statement
im really into sour stuff
flat harbor
hmm
gaunt latch
i need to get some roselle
sacred forge
i eat whole lemons sometimes
gaunt latch
lemons are shit
sacred forge
lemons are the best fruit
gaunt latch
no
roselle
is the best thing
tho it is a flower
not fruit
OOOO
have you tried Okra
😵💫
vivid halo
Most people don't know how to cook it without it getting all slimey
covert portal
have you tried Okra
what does it taste like?
also weren't you just a she/they yesterday.
dry leaf
can i post my prep chem questions here sometimes if i need help?
proud olive
Wonky looking jalapenos
neat lintel
can i post my prep chem questions here sometimes if i need help?
Join the Chem discord Brodie
proven hornet
yes
man if you practice 5 hours a day for 8 months youll get an 800 on the math section 💀
neat lintel
Huh, that’s more than enough if you study hard enough
south kelp
0 months is enough SAT math is 2ez
well I say that but I got a 770 on SAT math kek
unless u mean the subject test then I got an 800
neat lintel
we define everything in terms of sets right? how do we know there are enough sets for everything?
like in the way we construct reals how do we know there are enough sets so that it doesnt coencide with some r in R = some f:R->R
hich both are sets
or are they irrelevant
surreal sapphire
it doesnt matter in practice
but also if you look at the construction it doesnt happen
neat lintel
like it doesnt hinder me that 1(in R)=(x->x)
neat lintel
but also if you look at the construction it doesnt happen
hmm but in general it could happen if we dont pay attention to the construction in detail of 2 some very complicated objects
like idk only rational subset?of a unit sphere could be the same as a map zero mapping from Reals to Naturals
i guess it doesnt matter that they are equal
surreal sapphire
it doesnt matter, yes
neat lintel
man id love to prove some ridiculous thing using this idea like the unit sphere is bijective
idk how i construct reals tho i havent read it yet
surreal sapphire
a map is a triple, so its a set with 2 elements i think (following kuratowski), so this case doesnt happen either
there is also the thing that most objects can be constructed in multiple ways
but we dont care about that
we dont think as objects like that
neat lintel
there is also the thing that most objects can be constructed in multiple ways
yeah for some predefined construction
surreal sapphire
the only "weird quirk" i can think of is the empty tuple being the empty set
neat lintel
why not, proving "the unit sphere is bijective" seems fun
surreal sapphire
"is bijective"?
bright hill
man id love to prove some ridiculous thing using this idea like the unit sphere ...
Bijective to what?
neat lintel
Bijective to what?
its nothing serious i was just thinking if i could think of a sphere as a map then determine if it was bijective in some sense
ig unit disc is better suited for it but its a nonsensical idea so i wont dig deeper
gleaming grail
why isn't there a channel for algebra only linear-algebra?
woven whale
neat lintel
why isn't there a channel for algebra only linear-algebra?
Check #prealg-and-algebra
gleaming grail
thanks i see now
bright hill
its nothing serious i was just thinking if i could think of a sphere as a map th...
Bijective to what?
A set bijective to another set means there exists a map that's both injective and surjective between the two sets
gleaming grail
can you map spherical coordinates to cartesian coordinates?
bright hill
I don't know what a bijective set means
bright hill
can you map spherical coordinates to cartesian coordinates?
Yeah, ofc