Why $0 * \infty$ is undefined?

[mortal knoll]

Akash!

[scenic stirrup]

Why is $\frac{\infty}{\infty}$ undefined¿

[mortal knoll]

Akash!

[haughty wraith]

well it doesn't have to be undefined (like how in number space, inf/inf=1) but it is normally undefined because most systems treat infinity not as a number but as a idea of unending (even tho I personally don't like such systems)

[scenic stirrup]

i thought of a better one

[mortal knoll]

Akash!

[amber helm]

Well it’s undefined because there are many types that of infinities take for example ln(x)/x for x approaching infinity it converges to 0 because x—>x has a much faster growth rate than x—>ln(x) but now take e^x/x this diverges to infinity as x approaches infinity because it’s once again a question of growth rate, you can’t define the undefinable. Infinity is a concept not a number

[amber helm]

Wdym inf/inf =1? It’s undefined

Infinity is a way to study the behavior of certain mathematical objects as they get arbitrarily big or small you can’t treat it like a number

[trail fog]

define infty first then I'll tell you

[scenic stirrup]

i honestly don't know

[trail fog]

$(x=+\infty) \iff \forall v\in \bR, v<+\infty$

[mortal knoll]

Coffey, Slavic Taiga

[trail fog]

infinity isn't a number

@scenic stirrup

[trail fog]

it's a convenient way to say bigger or smaller(in the case of -infty) than any real number

you can easily exchange reals with naturals

or rationals or irrationals

won't matter much suite yourself

[scenic stirrup]

Well okey, but what is different infinities

[trail fog]

so in that sense, both functions :
f(x)=1/x
g(x)=1/x^2
tend to infty as x->0
but f(x)/g(x) -> 0

[scenic stirrup]

makes sense

[trail fog]

that's because some infinities are bigger than others

for example

the usuall infinity we deal with is the number of natural numbers

also called countable infinity

[scenic stirrup]

how is it countable?

[trail fog]

if there is a bijection from X to N then we say that X is countably infinite

so there's a countable number of naturals

integers

rationals

[scenic stirrup]

cool

[trail fog]

algebraic numbers (solution to some polynomial equation with rational coefficients)

but

[scenic stirrup]

so it still feels like infinity but it's actually countable

[trail fog]

No

It's infinitie.

we call this kind of infiniteness countably infinite

as we can count them

like number the elements in the set

what i mean is

there's a first natural number of we order it in some way

there's a first rational number

[scenic stirrup]

I actually have a doubt, a irrational number can be described by an infinite number of terms then why is it still an algebraic function and not a transcendental function?

[trail fog]

and so on so forth but there is not a first real number

[trail fog]

wdym by it can be described by an infinite number of terms

algebraic function?

[scenic stirrup]

sorry an irrational

[trail fog]

transcendental function??

[scenic stirrup]

Yes, an irrational function is an algebraic function but it can be described by an infinite number of terms

[trail fog]

well because there are more real numbers in any interval of R than there are naturals

[scenic stirrup]

so isn't it a transcendental function?

[trail fog]

wdym by function

[scenic stirrup]

A function is a relation between it's domain and the range

[trail fog]

yeah

wdym by irrational function

@scenic stirrup

[scenic stirrup]

i think I misunderstood the concept

[trail fog]

your terminology isn't native i think

what do you even mean

[scenic stirrup]

Man, aren't irrational functions used to describe irrational numbers right?

bye

i wanna study for exam

+close

[trail fog]

+close

f

[haughty wraith]

Yes that’s what I said