like if its even or odd ? but i'm not sure exactly how to guarantee that, and if it is even or odd, what does that mean?
#help-27
sweet steppe
stone stump
draw the function
from there you can easily see whether its odd or even
if at all
if its odd then it only has sin terms, so the a_ns are all zero
vice versa for even and b_ns
stone stump
draw the function
this does not mean that your drawing has to be good!
sweet steppe
this does not mean that your drawing has to be good!
okay i see
sweet steppe
from there you can easily see whether its odd or even
i dont understand
to me odd or even means 1 or 2
im not being sarcastic or joking here
like seriously i have no idea what it means in this sense
frozen aurora
a function f is even if f(-x) = f(x)
a function f is odd if f(-x) = -f(x)
sweet steppe
does the period matter?
frozen aurora
no
frozen aurora
yes
sweet steppe
but apparently its neither
frozen aurora
huh?
sweet steppe
as per the solution here
or is it a mistake on their end?
this might be me misundertanding something here ofc, i know readign solutions is not always the best way of going around thesse
sand dove
f(x) = x for x in [0,2pi), and 2pi-periodic is not odd
sweet steppe
here the range is f(x) = x [0, 2pi]
sand dove
odd = symmetric about the origin
For it to be odd, you need f(-x) = -f(x), meaning this
stone stump
if you have the "normal" function f(x)=x everywhere then its symmetric about the origin
but if you only have f(x)=x on some interval and then extend it periodically, you get your image from above which is not symmetric
sand dove
For example f(pi) = pi, but f(-pi) = pi, and not -pi
sweet steppe
ah i see
sand dove
So f is not symmetric around the origin
sweet steppe
so then [-2pi, 2pi] for x in f(x) = x is odd?
frozen aurora
yes
sweet steppe
ahh right okay
frozen aurora
this is odd
sweet steppe
so, if i may ask, since i am not good at drawing or sketching
can i substitute ?
or will there be values or issues that might arise with this
frozen aurora
substitute what
sweet steppe
the values on the boundary of the range
for example f(x) = x for [0, 2pi] i put f(0) and f(2pi) within the period of 2pi gives me 0 in both instances
frozen aurora
i would say the boundary is far from the best place to look at
sweet steppe
oh
sweet steppe
this is odd
right this makes sense
frozen aurora
for example f(x) = x for [0, 2pi] i put f(0) and f(2pi) within the period of 2pi...
for example the function you sent earlier is f(x) = x for [0, 2pi), note that this is a half open interval
sweet steppe
also the reason its used here is because sin(x) where x = -x is simply sin(x), but cos(x) where x = -x is -cos(x) (sorry worded wrong)
frozen aurora
for example the function you sent earlier is f(x) = x for [0, 2pi), note that th...
where you decide 2pi goes is a bit arbitrary
sweet steppe
for example the function you sent earlier is f(x) = x for [0, 2pi), note that th...
tho the range i have here is 0 <= x <= 2pi
not 0 <= x < 2pi
frozen aurora
regardless of where you set the value of 2pi, you get the same fourier series
frozen aurora
tho the range i have here is 0 <= x <= 2pi
eh maybe i am being nitpicky but yeah you get pointwise boundary issues when you say <=. but it doesn't matter that much
point is, learn to sketch functions
sweet steppe
i do know how to but i dont really understand the appeal of them
but i guess its fair enough
frozen aurora
play around in Desmos for some time and you'll get acquainted with them real quick
sweet steppe
so, the periodocity of a function is separate from whether it is odd or even, but it can affect the domain
frozen aurora
yes they are unrelated
sweet steppe
so odd or even if function has symettric domain, since period of this f(x) is [0, 2pi], it is neither
sweet steppe
play around in Desmos for some time and you'll get acquainted with them real qui...
sure ok
sweet steppe
so odd or even if function has symettric domain, since period of this f(x) is [0...
the reason it is neither is because the period is not symettric here [0, 2pi] vs for example [-2pi, 2pi]
frozen aurora
so odd or even if function has symettric domain, since period of this f(x) is [0...
yes. if your domain was [-pi, pi] then the picture would be like this one i sent #help-27 message
frozen aurora
it's like you are picking which part of f(x)=x to repeat periodically
sweet steppe
i see okay
and cos and sin are well defined in this manner so if we know this we can cancel out this behavior
for the fourier series
frozen aurora
if your function is even, we know that all sin terms have 0 coefficient: because cos is an even function and sin is an odd function, and a sum of function preserves their evenness/oddness
likewise if your function is odd, all cos terms have 0 coefficient
if it's neither even nor odd then you need to compute both, like in your case
sweet steppe
exactly
alright that makes a bit more sense
so, not much to do with the fourier series necessarily but is a short cut
frozen aurora
you can put it that way yeah
sweet steppe
but it makes sense, since i guess you are trying to emulate the behavior of a function as closely as possible
frozen aurora
yeah that's the point of fourier series lol
sweet steppe
oh is it
i dont even know what this is to be honest it just has a lot of marks so i was a bit worried, but it seems short
however it seems to make sense, the more you iterate over it the closer you get to the behavior of any f(x)
frozen aurora
assuming a bunch of constraints on "nice" f(x), yes, we can represent it as an infinite series of sin and cos terms
sweet steppe
i am not sure why it is alloted so many marks tho
mystic scarab
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sweet steppe
regardless of where you set the value of 2pi, you get the same fourier series
then here would my l be pi?
frozen aurora
yes
sweet steppe
.reopen
devout snowBOT
✅ Original question: #help-27 message
sweet steppe
even = symmetric about the y-axis
bc how is it symettric about the y axis here
mystic scarab
how is this even then?
Have you drawn it?
sweet steppe
i dont know how to sketch that
in a short amount of time
and it also seems zealous that i'd need to sketch or draw a function just to determine if its odd, even, or neither, or am i mistaken?
mystic scarab
i dont know how to sketch that
It's just a parabola 🤷♂️
sweet steppe
yea im sure its simple honestly but there must be a better way without having to draw stuff
mystic scarab
and it also seems zealous that i'd need to sketch or draw a function just to det...
If you have piecewise functions, the best way is drawing imo
sweet steppe
i am horrible at sketching
mystic scarab
yea im sure its simple honestly but there must be a better way without having to...
The problem is that there's the periodicity, hence the check "f(-x) = f(x)" must be done after finding the expression of the whole function, not only in the interval 0 to π
mystic scarab
i am horrible at sketching
Well, whether you like it or not , sketching skills have to be consolidated 🤷♂️
(of course I'm talking about simple functions, such as lines, parabolas, sin and cos, exponentials, unit steps, rectangle impulse, ramp, sign function)
stone stump
its a parabola thats opened downwards with roots at x=0 and x=pi
that should take a max of 3 seconds to draw
and then you extend it periodically
you dont have to draw the correct height or anything
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@sweet steppe Has your question been resolved?
manic sigil
Hey, I'm a little confused about something that messes up all my answers.
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manic sigil
<@&286206848099549185> Ayudame, por favor 🥺
real osprey
Have you tried doing everything in radians instead of degrees?
usually when there’s messy unit conversions radians might be a little better
doing
arctan(-0.5w)-0.1w = -π
Should give you w=16.887
manic sigil
doing
arctan(-0.5w)-0.1w = -π
Should give you w=16.887
Yeah I think that did work when I tried it but
- I'm afraid of switching to radians in the middle of my exam cause there's a good chance I'd forget to switch back, messing up the rest of the calculations
- My teachers and the book consistently write -180 degrees, without mentioning switching between rads and degrees, so I'm not sure if they both just skipped steps or what
Our graphs have one axis with rad/min and another with degrees too 😭
real osprey
That’s uhhhhh…
Well you can use π/180 to convert btw radians and degrees ig
The degrees sign is actually a unit in its own
manic sigil
Yeah that's what I tried to do I think
Maybe I'll write a note on my calculator to make sure I remember lol
real osprey
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calm blade
Im back
calm blade
cold haven
crude niche
!15m
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ionic harness
What problem is this related to
rain summit
can anyone remind me what's $a^n + b^n = ?$
woven radishBOT
1 divided by 0 equals Infinity
ionic harness
!occupied?
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ionic harness
Ah
rain summit
calm blade
What problem is this related to
Black bg
rain summit
$\alpha^8 + \beta^8$\
woven radishBOT
1 divided by 0 equals Infinity
rain summit
😭
rare kernel
sub x=alpha in ur quadratic and multiply with alpha^8 on both sides
and do the same with beta
u should be able to notice something
and get a Un term
calm blade
how did u get U8 in numerator and denom
Sub U10 =-sqrt U9 +U8
calm blade
Seems correct
Integer
stoic lotus
Wdym
calm blade
Integer answer
woven radishBOT
1 divided by 0 equals Infinity
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alpine python
Does $x^2 \equiv 1\pmod{p}$ imply $x\equiv \pm 1\pmod{p}$?
devout snowBOT
Does $x^2 \equiv 1\pmod{p}$ imply $x\equiv \pm 1\pmod{p}$?
woven radishBOT
Axe
supple knot
another way to see it could be to factor x^2 - 1
pseudo basin
Does $x^2 \equiv 1\pmod{p}$ imply $x\equiv \pm 1\pmod{p}$?
p prime? then yes.
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raven kayak
Hello, could someone check if this proof looks good please?
\begin{Definition}[Subset of a set]
Suppose $A$ and $B$ are sets. If every element in $A$ is also an element of $B$, then $A$ is a \emph{subset} of $B$, which is denoted $A \subseteq B$.
\end{Definition}
\begin{Definition}[Union of sets]
The \emph{union} of sets $A$ and $B$ is the set $A \cup B = { x : x \in A \text{ or } x \in B}$.
\end{Definition}
\begin{Definition}[Intersection of sets]
The \emph{intersection} of sets $A$ and $B$ is the set $A \cap B = { x : x \in A \text{ and } x \in B}$.
\end{Definition}
woven radishBOT
Mor Bras
raven kayak
\begin{Theorem}
Assume $A$, $B$ and $C$ are sets.
If $A \cup B = A \cup C$ and $A \cap B = A \cap C$, then $B = C$.
\end{Theorem}
\begin{proof}
Let $A$, $B$ and $C$ be sets.
Either $A = \emptyset$ or $A \neq \emptyset$.
Suppose $A = \emptyset$.
In which case $A \cap B = A \cap C = \emptyset$ holds.
Also, $A \cup B = B$ and $A \cup C = C$, and because $A \cup B = A \cup C$, we have that $B = C$.\
Now, suppose $A \neq \emptyset$.
If $B$ and $C$ are both empty, then $B = C = \emptyset$, which is what we wanted to prove.
Suppose now that one of $B$ or $C$ is empty and the other non-empty, or both non-empty.
Without loss of generality, suppose $B = \emptyset$ and $C \neq \emptyset$.
Then $A \cup B = A$.
And since $A \cup B = A \cup C$, we have that $A = A \cup C$.
On the other hand, $A\cap B = \emptyset = A \cap C$.
Because $A$ is non-empty, $A = A \cup C$, and $A \cap C = \emptyset$, it must mean that that $C = \emptyset$.
Thus, $B=C$.\
Lastly, suppose both $B \neq \emptyset$ and $C \neq \emptyset$.
Let $x \in B$.
Since $A \cap B$, we have that $x \in A$.
Then, because $A \cap B = A \cap C$ and $x \in A$, we have that $x \in C$.
Since $x \in B$ implies $x \in C$, by the definition of the subset, $B \subseteq C$.
A similar argument can be made by letting $x \in C$, showing that $C \subseteq B$.
Thus, since $B \subseteq C$ and $C \subseteq B$, we have that $B = C$.
Therefore, in any case, if $A \cup B = A \cup C$ and $A \cap B = A \cap C$, then $B = C$.
\end{proof}
woven radishBOT
Mor Bras
vital sedge
x in B doesn't imply x in A.
steady kettle
\begin{Theorem}
Assume $A$, $B$ and $C$ are sets.
If $A \cup B = A \cup C$ and ...
at the first line of the 3rd paragraph, i think
Since A⊂B
or i misunderstood
misty crest
wdym by since A \cap B we have that x in A
were you trying to say x in A \cap B
you said x \in B though?
raven kayak
at the first line of the 3rd paragraph, i think
Since A⊂B
Since A \cap B
misty crest
Since A \cap B
what does this even mean
since set
like thats all you said
what about A \cap B
raven kayak
misty crest
🤔
vital sedge
we take x in B, then as A intersects B, we have that x is in A?
how does that work twin
raven kayak
I don't even know at this point, let me check
\begin{proof}
Let $A$, $B$ and $C$ be sets.
Either $A = \emptyset$ or $A \neq \emptyset$.
Suppose $A = \emptyset$.
In which case $A \cap B = A \cap C = \emptyset$ holds.
Also, $A \cup B = B$ and $A \cup C = C$, and because $A \cup B = A \cup C$, we have that $B = C$.\
Now, suppose $A \neq \emptyset$.
If $B$ and $C$ are both empty, then $B = C = \emptyset$, which is what we wanted to prove.
Suppose now that one of $B$ or $C$ is empty and the other non-empty, or both non-empty.
Without loss of generality, suppose $B = \emptyset$ and $C \neq \emptyset$.
Then $A \cup B = A$.
And since $A \cup B = A \cup C$, we have that $A = A \cup C$.
On the other hand, $A\cap B = \emptyset = A \cap C$.
Because $A$ is non-empty, $A = A \cup C$, and $A \cap C = \emptyset$, it must mean that that $C = \emptyset$.
Thus, $B=C$.\
Lastly, suppose $B \neq \emptyset$ and $C \neq \emptyset$.
Let $x \in A \cap B$.
Then, by the definition of the intersection, we have that $x \in A$ and $x \in B$.
Then, because $A \cap B = A \cap C$, we have that $x \in A \cap C$ and, by the definition of the intersection,
$x \in A$ and $x \in C$.
Since $x \in B$ implies $x \in C$, by the definition of the subset, $B \subseteq C$.
A similar argument can be made by letting $x \in C$, showing that $C \subseteq B$.
Thus, since $B \subseteq C$ and $C \subseteq B$, we have that $B = C$.
Therefore, in any case, if $A \cup B = A \cup C$ and $A \cap B = A \cap C$, then $B = C$.
\end{proof}
misty crest
you said x \in A \in C
think you mean x \in A \cap C
where did you establish that B \subset C?
woven radishBOT
Mor Bras
raven kayak
where did you establish that B \subset C?
Because x is in both B and C
raven kayak
Certainly, and because $x \in A \cap B$, it means that $x \in A$ and $x \in B$
woven radishBOT
Mor Bras
misty crest
and
raven kayak
That same element is in $A \cap C$ because $A \cap B = A \cap C$, which means $x \in A$ and $x \in C$.
misty crest
this would just say that if all three sets are nonempty then B and C have a nonempty intersection
woven radishBOT
Mor Bras
raven kayak
That same element is in $A \cap C$ because $A \cap B = A \cap C$, which means $x...
For sure
misty crest
yes i agree, if x is in A \cap B then x is in B and x is in C so x is in B \cap C which tells us B \cap C \neq \emptyset
where are you getting B \subset C from this
raven kayak
From the definition of subset, since x in B implies x in C, this means B is subset of C
misty crest
what
raven kayak
what
misty crest
the definition of subset is not "if there exists x in B such that x is in C then B is a subset of C"
it has to be true for all elements of B
which you have not shown
you've only shown that the elements of B that are also in A are in C
what about the elements in B that aren't in A?
raven kayak
Yes, I see
misty crest
the fact that you didn't use A \cup B = A \cup C in your argument at all should be a major red flag
why else would they give you that information
i have to go eat
but to check your work you should get B = (A \cap B) \cup (A^c \cap B) and you've already covered the case that x is in A \cap B so for the case of x \in A^c \cap B you just need to argue that x is in C which is clear since if x is in A^c \cap B then x \in B so x \in A \cup B = A \cup C but x \notin A so x \in C
i'm sure someone else will check your final wording
have a nice night sir
raven kayak
i'm sure someone else will check your final wording
Surely, I didn't use that. Besides all of this, I have been struggling with this proof all day
devout snowBOT
ionic harness
\begin{Theorem}
Assume $A$, $B$ and $C$ are sets.
If $A \cup B = A \cup C$ and ...
Hint: contradiction would be your friend here
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raven kayak
Hint: contradiction would be your friend here
Certainly, but right now I'm proving directly
devout snowBOT
Certainly, but right now I'm proving directly
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devout snowBOT
lunar harbor
good
drifting sierra
Yes, it is
fickle moon
Yes, it is
thank u nel
drifting sierra
The range of g "goes into" the domain of f
So if they don't overlap, there's no domain for (f o g)
fickle moon
So if they don't overlap, there's no domain for (f o g)
ohhhh
i see
thats a good explanation
thank u
.close
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granite arch
is this a typo
devout snowBOT
is this a typo
supple knot
$\varphi$ is just a different font of $\phi$
woven radishBOT
riemann
still tangle
It's pretty bad formatting to just switch it up suddenly, though
It seems to be the same map though
granite arch
It seems to be the same map though
- is because its the binary operation on Z right
i was so confused
devout snowBOT
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sweet steppe
for a fourier series, what is the best algebraic way to test whether a function is even or odd?
devout snowBOT
for a fourier series, what is the best algebraic way to test whether a function ...
sweet steppe
or neither
sand pumice
the easiest way is to simply plug x and -x
sweet steppe
no this doesnt work for all
for example f(x) = x(pi-x)
if you plug -x you get x(x-pi)
but then i have the constraint that ther periodicity of this function is [0, pi]
so with this, apparently, it becomes an even function
stone stump
dude just learn to draw
sweet steppe
no
stop telling me to draw stuff
im not spending 10 minutes drawing something for 0 marks
solar gyro
f(-x)=-f(x) odd and f(-x)=f(x) is even.
sweet steppe
i mean, if its simple i can, but they get more complicated
sweet steppe
f(-x)=-f(x) odd and f(-x)=f(x) is even.
the function above is even but if you do these tests the result doesn't persist
sweet steppe
you end up with x(x-pi)
now, since the periodicity is pi, technically it becomes f(x)
but this does not work if it gets more complex
so i am curious on what the algebraic way of solving this is
solar gyro
this isnt a trigonometric function necceseraly right
cus it depends on the name when it is
hm let me think
sweet steppe
this isnt a trigonometric function necceseraly right
meh not necesarily
for example then
f(x) = mod(sin(x)) is obviously even
so thats great
but then something like the above is the tricky one
i dont understand how to get a well defined way to see if its even or odd
dim perch
for example `f(x) = x(pi-x)`
how is this function even? parabola with roots at 0 and pi, if i sub -x, i get
-x(pi - (-x)) or -x(pi + x)?
that function is neither odd nor even
you can extend it to be an even or odd function i guess
but even so, restricting your example to 0 to pi doesn’t make it even or odd whatsoever; the only thing i can maybe say is that its symmetric about x = pi/2?
sweet steppe
you can extend it to be an even or odd function i guess
no its even
I have absolutely no idea
that is why i am asking
If you look at the graph dont get me wrong, it is even
dim perch
oh gotcha, its periodic over [0, pi] and they did an even continuation
did they specify that they’d extend it to an even function?
dim perch
yeah that is strange
solar gyro
can u send the question if possible
dim perch
theyd usually tell you how they want you to extend it
sweet steppe
yes definitely sorry
i will clarify again, my question here more or less is given the form of this type of question, without sketching, is there any viable way for me to clearly this f(x) is even, odd, or neither?
overall i understand how to do the f ourier series. if anything, it is quite easy
devout snowBOT
@sweet steppe Has your question been resolved?
solar gyro
lets see
yk cosine is an even function right
im not rly a pro in interval so all i can say is sin is odd and cos is even
but i think u already considered those
i think fx shd be even too
sweet steppe
yes
solar gyro
still in the progress of learning interval sorry i cant be much of a help🙏
solar gyro
i will clarify again, my question here more or less is given the form of this ty...
usually you can tell by this one i mentioned
solar gyro
f(-x)=-f(x) odd and f(-x)=f(x) is even.
.
its neither you can see
its possible for it to be neither
as far as i know
let me check the accuracy
basically it has no symmetry
solar gyro
let me check the accuracy
x+1
x^2+x
or sinx+cosx
neither of them are odd or even
maybe it shd be smth related to this?
sweet steppe
usually you can tell by this one i mentioned
correct
but this does not always work
i will give this example here
Take this: f(x) = x
this is odd by default
but then if you add that f(x) has a period of 2pi, no longer odd or even (its neither)
bc u end up with this
solar gyro
bc u end up with this
yes ur right
sweet steppe
u are also right, neither odd or even can be the case
so then my question for the pros is
is there a decent way of checking this, specifically for the fourier series if needs be?
currently i have seen that if you have given:
f(x) has a period of [0, T) you can simply test f(T - x)
but i feel this would fail if symettry id [-T/2, T/2)
but then the default f(-x) would work there
so idk whats happening
solar gyro
hmm arent we basically changing the symmetry
like if we extend it w the right interval
it shd stay as odd
for f(x)=x
so my thought was isnt that a complete exception where we extend the period asymetrically
solar gyro
it basically forms a sawtooth wave
thats what we call it in physics im not sure if its the same here
idk if this wd help
let me watch it real quick
i think its helpful
sweet steppe
it basically forms a sawtooth wave
exactly yea
solar gyro
idrk anymore lets wait for a pro to answer
solar gyro
yes
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marble hearth
Where did I go wrong here?
devout snowBOT
Where did I go wrong here?
marble hearth
I got $\frac{100a^{12}}{b4}$ instead of $\frac{-100a^{12}}{b4}$
woven radishBOT
Vortac
lusty sapphire
Where did I go wrong here?
$a^{-1}(-a)^{-3}\ne(-a)^{-4}$
woven radishBOT
SWR
lusty sapphire
What's the rule for that?
Well one is a and the other is -a. You primarily need to fix that
General rule is $a^ba^c=a^{b+c}$. You can't mix negatives and positives
woven radishBOT
SWR
marble hearth
That I know, but what do I do in the case of $(-a^b)a^c$?
woven radishBOT
Vortac
lusty sapphire
$(-a)^{-3}=-(a^{-3})$
woven radishBOT
SWR
marble hearth
I still don't get it, how would I know to move the parens like that?
Do I do the same thing for the $b^6$ and $(-b)^{10}$?
woven radishBOT
Vortac
devout snowBOT
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marble hearth
.close
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dark talon
I still don't get it, how would I know to move the parens like that?
Sounds like your problem is with the negative sign
If you have a negative sign, that means you have a multiplication by -1
marble hearth
I think I figured it out
dark talon
When you deal with exponents go like this:
if even remove the negative sign
If odd move it outside the parens
For example:
(-b)^8 = (-1)^8 * b^8 = 1 * b^8
= b^8
(-a)^5 = -1^5 * a^5 = -1 * a^5 = -a^5
marble hearth
If the exponent is odd, we move the negative outside the parens, ie: $(-b)^{-3} = -(b^{-3})$
woven radishBOT
Vortac
dark talon
Yeah you got it
If you dont mind, share your final result after, so we could check if it’s correct
marble hearth
marble hearth
When you deal with exponents go like this:
if even remove the negative sign
If...
So just to confirm, $(-b)^{-3} = -(b^{-3})$ while $(-b)^{-4} = (b)^{-4}$?
woven radishBOT
Vortac
dark talon
Yes
marble hearth
Ok that makes sense
dark talon
Why did you make a^(-1+3) ?
The other a has exponent -3 not + 3
Nvm
Got it
Correct but note that you kept the -b in the steps when you shouldve made it +b
devout snowBOT
Available help channel!
vivid hatch
Does anyone know why this works : 1/2absin(V)
devout snowBOT
Does anyone know why this works : 1/2*ab*sin(V)
devout snowBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
pseudo basin
Does anyone know why this works : 1/2*ab*sin(V)
don't half-state formulas
steady kettle
i think so
vivid hatch
don't half-state formulas
I am a idoit
vivid hatch
Assume it's triangle area one
Ty
pseudo basin
I am a idoit
being mean to yourself is not good for the soul
vivid hatch
being mean to yourself is not good for the soul
Idiot is not that big of hurtful thing, i will say sloppy
devout snowBOT
Available help channel!
gloomy geyser
I know this is a mathematics discord but i cant seem to find a physics discord so i am just going to hope that a guy who knows physics can help me, i will close this if you warn me or something. Problem : i used desmos to graph a current vs angular frequency graph with everything constant and varying time. as i expect as time goes on the graph becomes a seemingly smooth hill as the circuit achieves equilibrium with its peak at resonant frequency but as the time approaches 4100 seconds the graph becomes less detailed, i cannot explain why this happens, maybe its desmos calculation error stuff or something else.
devout snowBOT
I know this is a mathematics discord but i cant seem to find a physics discord s...
gloomy geyser
willow helm
I know this is a mathematics discord but i cant seem to find a physics discord s...
#old-network Physics is the second from the top 🙂
fossil locust
I know this is a mathematics discord but i cant seem to find a physics discord s...
the answer is indeed "Desmos calculation error stuff"
they are using floating-point numbers to plot the graph and those inherently have error
gloomy geyser
they are using floating-point numbers to plot the graph and those inherently hav...
are you sure about that or am i missing something ?
fossil locust
are you sure about that or am i missing something ?
yes, I'm sure that's the reason
it's to do with the loss of numerical precision
devout snowBOT
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Available help channel!
stiff raven
⇒ y ∉ (A ∩ B)
⇒ y ∉ A or y ∉ B
can someone explain this step
devout snowBOT
⇒ y ∉ (A ∩ B)
⇒ y ∉ A or y ∉ B
can someone explain this step
pseudo basin
de morgan's law
y ∉ A ∩ B means NOT(y ∈ A ∩ B) means NOT(y ∈ A and y ∈ B)
when you apply de morgan's law the and becomes or
stiff raven
i see
stiff raven
when you apply de morgan's law the _and_ becomes _or_
any idea why tho
pseudo basin
why what
stiff raven
the and becomes or
stiff raven
yea
pseudo basin
imagine a lightbulb connected to two switches, in such a way that it lights up when at least one switch is on.
that is, lightbulb on <=> (#1 on OR #2 on)
what can you say about the switches if you see the lightbulb being OFF?
stiff raven
what can you say about the switches if you see the lightbulb being OFF?
both of them are turned off
wait i think i get it
let me think thru this for a second
pseudo basin
there was going to be a second part to this but ok
willow helm
probably nice
willow helm
i don't understand what the abbreviation "nc" stands for
everything but using the letters required is 'cool' now!
pseudo basin
the second part is this
imagine another lightbulb also hooked up to two switches but they BOTH need to be on to turn the lightbulb on
in other words, now we have
lightbulb on <=> (#1 on AND #2 on)
if the lightbulb is OFF what can you say about these switches
stiff raven
if the lightbulb is OFF what can you say about these switches
either of them are turned off or they both are turned off
stiff raven
everything but using the letters required is 'cool' now!
sorry if it was offending
willow helm
sorry if it was offending
No, not at all. Was just making a joke 🙂
pseudo basin
either of them are turned off or they both are turned off
...which is exactly captured with an or.
stiff raven
...which is exactly captured with an _or_.
so the second part would come along to AnB's complement = AUB
woven radishBOT
Ann
pseudo basin
not A ∪ B
stiff raven
**Ann**
but in that case they both would be turned off
OHH
so turned off means complement
in this case right?
pseudo basin
was this genuine or sarcastic
stiff raven
genuine
i've got a test tomorrow and i'm shaking on my boots right now
so any immediate help is much appreciated :D
errant hinge
I'm not sure if asking for physics help is legal but pleasee
devout snowBOT
I'm not sure if asking for physics help is legal but pleasee
errant hinge
so far I think that ii is correct because the person's back is pushing against the wall and the wall is pushing back on them
however the side view things make no sense
the floor has dropped so no forces should be coming from floor
and figure iv should have weight because the person still has weight
devout snowBOT
@errant hinge Has your question been resolved?
weary arch
so far I think that ii is correct because the person's back is pushing against t...
Sounds all right to me
errant hinge
Sounds all right to me
what about iii and iv
weary arch
Everything you said
errant hinge
there is no option for just ii
weary arch
Yes, here they are not asking for a full list of all the forces, just which ones are correct
In fact there are missing horizontal forces too in ii
errant hinge
which horizontal force is missing
weary arch
Centrifugal forces? He is being spun
errant hinge
centrifugal force is not a real force
this question is poorly made
there should not be any net force on the person or wall
there should be no force coming from the floor
weary arch
Right yeah no it's only in the rotating ref frame
weary arch
this question is poorly made
there should not be any net force on the person or ...
But yeah he's not moving vertically
unborn osprey
I'm not sure if asking for physics help is legal but pleasee
2 is right
obsidian torrent
Weight wouldn't make sense if the floor is dropping
but yh 2nd seems right to me too
Tho you're right there's no centripetal force
unborn osprey
weight would always be there right?
obsidian torrent
yes but there's not only weight
I mean this is a case is weightlesness
Because it's been spun so fast the weight is negated
devout snowBOT
@errant hinge Has your question been resolved?
devout snowBOT
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Available help channel!
north hound
devout snowBOT
north hound
If ABC is any triangle and D is the midpoint of BC and E is any point on AD and F is the point of intersection of BE and AC and G of CE and AB, prove that GF || BC.
!status
devout snowBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
wheat pawn
S is not a point in the graph given
round raptor
S is not a point in the graph given
G he means
north hound
Yes, that proves it, but is it the best medium to prove that GF || BC? Because GF | | BC follows immediately from FE/EB = GE/EC.
azure parrot
Yes, that proves it, but is it the best medium to prove that GF || BC? Because G...
GF/EB?
north hound
My bad. It should be FE/EB = GE/EC
azure parrot
We can't directly show GF||BC with just GE/EC=FE/EB
But it helps us get AG/AB=AF/AC
Which is sufficient
north hound
It shows that the triangles GEF and CEB are similar by the SAS theorem of similarity, and hence the angle EFB = angle EBC.
azure parrot
Fair
I was going to use Thales
But okay that works
now it's your job to show GE/EC=FE/EB
azure parrot
I have no idea what you meant by now
north hound
Not necessary to show first prove that GE/EC = FE/EB. There could be an easier way.
omg
azure parrot
azure parrot
GE/EC=FE/EB ratio is quite obvious
But hey
If you have another way then
Do that
north hound
GE/EC=FE/EB ratio is quite obvious
How so
azure parrot
How so
||Area(EAB)=Area(EAC)||
On the other hand ||Area(EAB)=EG/GC Area(ABC) ||
And ||Area(EAC)=EF/FB Area(ABC)||
devout snowBOT
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Available help channel!
neon wagon
hello so
winter torrent
i would assume each face is equal probability
round raptor
yes equally likely until stated
neon wagon
i would assume each face is equal probability
wtf is wrong here
round raptor
wtf is wrong here
can't see anything cancelled
neon wagon
can't see anything cancelled
wdym cancelled
round raptor
wdym cancelled
scribble
round raptor
why was it that
mystic scarab
why is 1-6/8 wrong
Where does it say it is wrong?
I don't know what those red writings mean
round raptor
hiw did you get 1/8
mystic scarab
why is it 16
16 is 4•4, i.e. the number of possible outcomes (n1, n2)
Which couples give a product ≤ 4? There's not only 4 of them, rather 8
(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (3, 1), (4, 1)
Therefore P(A) = 1 - 8/16 = 8/16 = 1/2
neon wagon
hiw did you get 1/8
4 on the one cube 4 on the other
or does
fuckkkkkk
no way i forgot this simple thing
round raptor
Which couples give a product ≤ 4? There's not only 4 of them, rather 8
(1, 1), ...
ig typo 3,1 instead of 1,4
neon wagon
i got a D+ i wouldve had a C- if i did this right
round raptor
i see you translated this what lang was it
mystic scarab
ig typo 3,1 instead of 1,4
Uh yeah thx. Then I also noticed I forgot other two pairs lol
neon wagon
i see you translated this what lang was it
german
neon wagon
Which couples give a product ≤ 4? There's not only 4 of them, rather 8
(1, 1), ...
it says greater than 4 tho
devout snowBOT
@neon wagon Has your question been resolved?
devout snowBOT
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Available help channel!
rustic apex
How to work out gradient with just the y intercept and a set of co odinates
crystal dawn
devout snowBOT
@rustic apex Has your question been resolved?
abstract plover
devout snowBOT
rustic apex
.reopen
devout snowBOT
✅ Original question: #help-27 message
rustic apex
.close
devout snowBOT
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Available help channel!
hollow warren
I'm confused on how they got the answer i've factorised it and and put it on the scale but i kinda still dont understand since my original answer was 4<x<5
devout snowBOT
I'm confused on how they got the answer i've factorised it and and put it on the...
pseudo basin
4<x<5 is preciselty where your curve is BELOW the x-axis meaning the quadratic is LESS than zero
round raptor
I'm confused on how they got the answer i've factorised it and and put it on the...
What you did is the exact opposite
hollow warren
i know that its depended on the symbol of <> and whether its above the x axis but cant remember which is which
pseudo basin
big y go up
above x axis means y>0
below means y<0
like a thermometer
have you seen a thermometer in your life before? like those vertical things with a red line that tells the temperature
pseudo basin
ok and you know how high temperatures mean the red line climbs up
its the same with the y axis on a graph
big y. go up.
i am literally saying it in the most caveman speak way possible
devout snowBOT
@hollow warren Has your question been resolved?
trim oar
Hi is there anyone here who can help me with pre calc ? My send options don’t work & id prefer if we can communicate through insta mine is: Catsaresocuteyk please if you can help send me a Dm request or follow It’ll be much appreciated my test is tomorrow thank you sm
devout snowBOT
Hi is there anyone here who can help me with pre calc ? My send options don’t wo...
uncut crow
help through insta is crazy
cold haven
mystic scarab
it says greater than 4 tho
Sure, then I took the complent
supple knot
help through insta is crazy
Instagram supporting latex. We're living in the future.
stoic lotus
help through insta is crazy
Meta is an extrimist organization (same as ISIS) in Russia 👍
devout snowBOT
@trim oar Has your question been resolved?
devout snowBOT
@trim oar Has your question been resolved?
devout snowBOT
@trim oar Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
chrome sundial
hey guys
proud perch
!da2a
devout snowBOT
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
chrome sundial
im really hard to work with btw so u gotta be locked in to help i dont know a word
idk if this whole page is right
devout snowBOT
@chrome sundial Has your question been resolved?
chrome sundial
no
devout snowBOT
@chrome sundial Has your question been resolved?
devout grotto
idk if this whole page is right
looks fine to me
devout grotto
my dad lowkey did it
which one
chrome sundial
all
devout grotto
pick one
chrome sundial
7
devout grotto
what specifically are we not understanding
chrome sundial
like I don’t know how to answer the problems at all like ABC and D
devout grotto
bc i can’t read your mind here, so i need to know what is tripping you up
if you said your dad did it i would strongly recommend asking your dad for help
devout grotto
like I don’t know how to answer the problems at all like ABC and D
do we understand all the words on the page
chrome sundial
bro he uses chat gpt and doesn’t explain good and writes just to write
he barley knows how
devout grotto
bro he uses chat gpt and doesn’t explain good and writes just to write
ok maybe not then
do you understand all the words on the page
chrome sundial
i think
devout grotto
k so what is the holdup
in other words: what specifically are you asking for help understanding?
chrome sundial
how to answer number 7
devout grotto
!status
devout snowBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
i suspect ||1||
chrome sundial
chrome sundial
yes
devout grotto
kk, so talk to me about the answer for 7a. which result on the chart i just sent would give us that answer?
chrome sundial
none
chrome sundial
alterniste interior
devout grotto
yes that is true
does anything apply to (b)? why/why not?
and don’t just read off the answers, try and articulate
devout grotto
can you use the chart to understand the rest of 7?
sounds like you’ve a midterm coming up so you may have to memorize the above chart, but such is maths
chrome sundial
I have a question is ABC and D like “rules” to figure out if the lines are parallel or not?
i’m still very confused on how to determine if the lines are parallel
and do we just put alternate interior and like what they are and stuff
devout grotto
i’m still very confused on how to determine if the lines are parallel
if the angles match the lines are parallel
devout grotto
have we seen something like this chart before?
like here the fact that angle d = angle e means that the lines are parallel
the result goes both ways, so || lines imply matching angles AND matching angles imply parallel lines
chrome sundial
so the answers yes, no, yes, yes, no
devout grotto
yesn’t — remember that the question is describe AND JUSTIFY
so you have to show your work
but the answers you have are right
chrome sundial
b has nothing
devout grotto
no need to justify a null answer — nothing to indicate || lines
chrome sundial
yeah i guess
i don’t have to relearn everything to a perfect 100 percent i’ll just write what’s on the study guide and hope for the best
devout grotto
khan academy is super helpful, here’s a video https://www.youtube.com/watch?v=H-E5rlpCVu4
go watch that and come back if you need any other clarifications
devout grotto
!done
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
devout snowBOT
@chrome sundial Has your question been resolved?
pale schooner
I know it feels stupid but how do I prove |Q|=2 (formally)?
devout snowBOT
I know it feels stupid but how do I prove |Q|=2 (formally)?
pale schooner
I really want to write "it's easy to see that |Q|=2"
void fox
Could you provide a translation of the question?
pale schooner
Could you provide a translation of the question?
1 min
I'm on (a)
It feels like if I prove there's no even number which is odd (and the opposite). But we didn't learn something like that
Maybe I can write it as a union of two singletons and we proved singletons have 1 element
I think I got it
devout snowBOT
@pale schooner Has your question been resolved?
vagrant fulcrum
Given point A(1;0;3) in Oxyz. Write the function of line (delta) that goes through point A and intersect Ox, Oz at M, N so that vct AM = 2.vect AN?
devout snowBOT
Given point A(1;0;3) in Oxyz. Write the function of line (delta) that goes throu...
vagrant fulcrum
I already found the coords of N and M
N(0, 0, t) and M(c, 0, 0)
and now i have two variable
and i only have one function which is vct AM = 2 vct AN
where do i find more function so that i can find t and c?
azure parrot
and i only have one function which is vct AM = 2 vct AN
not really
you're dealing with vectors
You actually have more than an equation
vagrant fulcrum
i.. dont know if it solve anythin- oh wait
ahhh my bad i forgot
right right i figured it out
but eh once i found M and N
i can just
create whatever direction vector i want to create with the 3 points?
and then use that vect to write the func?
azure parrot
create whatever direction vector i want to create with the 3 points?
Not sure what you meant but you can find vec AM and vec AN in term of m and n ( 2 variables )
and use that to make a system of equations as I said
vagrant fulcrum
Not sure what you meant but you can find vec AM and vec AN in term of m and n ( ...
well i meant i can find the t and c now
so i can just create a direction vector
and then use that to write the function of delta
azure parrot
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Available help channel!
solar gyro
can someone help me w this? integral-area usage
devout snowBOT
can someone help me w this? integral-area usage
solar gyro
ik how to explain it thru derivative
but i need to know how can one apply integral to these kind of derivative graphs
its an increasing derivative since its above ox
.close
devout snowBOT
tender wharf
its an increasing derivative since its above ox
derivaitive is not increasing function is increasing
tender wharf
can someone help me w this? integral-area usage
if the integral is negative means the function was overall decreasing
devout snowBOT
Available help channel!
lyric matrix
👋 help me
woven radishBOT
cold haven
flat sandal
I believe you can simply use the quadratic formula here and figure out the roots by the conditions
lyric matrix
I believe you can simply use the quadratic formula here and figure out the roots...
Try if u can but I don’t think so it is that easy
round raptor
Try if u can but I don’t think so it is that easy
it seems so it is
round raptor
try quadratic
lyric matrix
try quadratic
Abbé sale karto liya
round raptor
Abbé sale karto liya
ha toh dikha
lyric matrix
ha toh dikha
Kya ?
gloomy aurora
,, \sec(\theta) \pm |\tan(\theta)|
think you meant $\pm$
woven radishBOT
Annie Maqionde
round raptor
yh i'm bad at latex
woven radishBOT
scoob
flat sandal
**scoob**
It's what you get from the quadratic formula
Then those two roots you see which is which by the conditions given
round raptor
,, \sec^{2}(\theta) - 1 = \tan^2(\theta)
flat sandal
Note that it's on the IV quadrant and it says alpha 1 > beta 1
woven radishBOT
scoob
lyric matrix
Oh oh so quadratic was to be used
flat sandal
Yeah, the b^2 - 4ac gives 4sec^2theta - 4 which can be factored as 4(sec^2theta-1) which can be turned into that tan^2theta term
lyric matrix
U all could have told me rather than trying to give the solution
round raptor
U all could have told me rather than trying to give the solution
told you what
gloomy aurora
As helpers, our duty is to facilitate independent problem-solving rather than giving the answer ourselves.
north hound
AD is both an angle bisector and a median in a triangle ABC where D lies on BC.
drifting sierra
What have you tried?
north hound
I know the theorems of congruence, but they do not apply well here.
drifting sierra
Why?
north hound
There are only two common sides and a pair of equal angles not between the common sides - this is SSA, which is not a theorem of congruence.
drifting sierra
True, so you need to find a way to say that ADB and ADC are right angles
I have a funny way to prove this but another simpler way is by contradiction using the perpendicular bisector
Not sure that's the simplest way though, others might want to weigh in
winter patrol
are you allowed to apply sine rule/law?
drifting sierra
Oh yeah that's more straightforward
devout snowBOT
@north hound Has your question been resolved?
hexed beacon
“Let M be a matrix that is in RREF with m columns and n rows. Suppose also that m < n. Prove that the bottom row of consists of only zeros. Hint: think about the maximum number of leading 1s that can have.”
Intuitively I know that the maximum number of leading 1s is n, but I’m not entirely sure how to say it, and I can also imagine why it is that the bottom row must contain all zeroes, since I picture something like what’s pictured below, but I’m not entirely sure how to say it. Any guidance is much appreciated.
devout snowBOT
“Let M be a matrix that is in RREF with m columns and n rows. Suppose also that ...
safe perch
can someone help me
void fox
!occupied
devout snowBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
void fox
“Let M be a matrix that is in RREF with m columns and n rows. Suppose also that ...
Since the leading 1s form a staircase there can be at most n nonzero rows
hexed beacon
Then after that could I say "As there are more rows than columns, and any row of all zeroes must be at the bottom, the bottom row must be all zeroes," or do I need something else?
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Available help channel!
devout snowBOT
sullen osprey
Does anyone have any advice on doing these?
This is what I did for the part a
A - Authorise
B - Blacklist
T - Temp-pass
E - Employee
∀x(A(x)↔(¬B(x)⋀ (T(x)) ⋁ E(x))
I'm not really sure how to do CNF, theres no good resources online and for the 2. I'm just very confizzled 😕
drifting sierra
This is what I did for the part a
A - Authorise
B - Blacklist
T - Temp-pass
...
Your parentheses are off
drifting sierra
TeX it
sullen osprey
What is that?
drifting sierra
Write it in LaTeX
drifting sierra
Time to learn: begin your message with ,,, and use \forall, \iff, \neg, \land, and \lor
sullen osprey
,, \forall x (A(x) <-> (\negB(x)) \land (T(x)) \land E(x))
woven radishBOT
Vaynn
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sullen osprey
,, \forall x (A(x) \iff (\negB(x)) \land (T(x)) \land E(x))
woven radishBOT
Vaynn
\begin{gather*}
\forall x (A(x) \iff (\negB(x)) \land (T(x)) \land E(x))
\end{gather*}
```Compilation error:```! Undefined control sequence.
<argument> \forall x (A(x) \iff (\negB
(x)) \land (T(x)) \land E(x))
l.51 \end{gather*}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```
drifting sierra
It's not understanding \negB
sullen osprey
i dont understand
oh
,, \forall x (A(x) <-> (\neg B(x)) \land (T(x)) \land E(x))
woven radishBOT
Vaynn
lyric hornet
(\forall x(A(x)\iff\neg B(x)\land (T(x))\lor E(x)))
drifting sierra
Anyway, do you see the pair of parentheses that are misplaced and not doing anything
sullen osprey
let me have a look
drifting sierra
\(\forall x(A(x)\iff\neg B(x)\land (T(x))\lor E(x))\)
You have one too many parentheses
lyric hornet
would appear I do
sullen osprey
Maybe I don't need the one around the neg B
because its isolated using the and and the iff already
idk
woven radishBOT
ΠαϳαμαΜαμαΛλαμα
sullen osprey
was i right?
drifting sierra
No it's still not quite correct
sullen osprey
oh 😔
im not sure I learnt first-order logic myself i couldn't attend lesson because of circumstances
drifting sierra
You need to pay attention to details when doing logic
The T(x) is in parentheses but it's just a single term, so it doesn't need them
However, you need parentheses to show which one of the AND and OR is applied first
drifting sierra
Typically the AND is considered to have higher precedence, which in this case makes your formula incorrect
sullen osprey
wait so what have i done wrong
I shouldn't have brackets by anything surrounding AND because it is assumed higher anyway?
drifting sierra
Well in your LaTeX you wrote AND twice instead of AND and OR like in your first message
But anyway:
,, \forall x (A(x) \iff \neg B(x) \land \textcolor{red}{(}T(x) \lor E(x)\textcolor{red}{)})
woven radishBOT
Nel
sullen osprey
Well in your LaTeX you wrote AND twice instead of AND and OR like in your first ...
oops
yeah lol
So I dont need the red brackets?
drifting sierra
You do
sullen osprey
oh
drifting sierra
Otherwise we don't know which of the AND and the OR is applied first
,, \forall x (A(x) \iff (\neg B(x) \land T(x)) \lor E(x))
woven radishBOT
Nel
drifting sierra
This is not the same formula
sullen osprey
im confused
so what are u saying i have to do to fix it, I have to make sure AND is applied first?
drifting sierra
... no, the question says "[...] not blacklisted and the user either has a temporary pass or is an employee"
Which one is applied first?
sullen osprey
or..?
drifting sierra
Right, so you need parentheses around that one
drifting sierra
No that's the same as T(x) V E(x)
sullen osprey
oh maybe I get rid of the two external brackets
drifting sierra
What
sullen osprey
idk
drifting sierra
These aren't even paired