[math]e = lim_{xtoinfty} (1+frac{1}{x})^x\

[math]e = \lim_{x\to\infty} (1+\frac{1}{x})^x\\
e = (1+\frac{1}{\infty})^\infty\\
0 = \lim_{x\to\infty} \frac{1}{x}\\
0 = \frac{1}{\infty}\\
e = (1 + 0)^\infty\\
e = 1^\infty\\
\blacksquare[/math]

Attached: leonhard-euler-gets-his-tight-kurt-godel-succ-by-in-8570013.png (500x766, 187K)

Other urls found in this thread:

mathworld.wolfram.com/Infinity.html
wolframalpha.com/input/?i=1^infinity
twitter.com/SFWRedditImages

[math]
e^x= \frac{x^0}{0!}+ \frac{x^1}{1!}+ \frac{x^2}{2!}+ \frac{x^3}{3!}+ \frac{x^4}{4!}+ \cdots
[/math]

>Thinks taking a limit means plugging in the limiting value to the variable you're taking the limit of
>Thinks 1/infinity alone has a legitimate mathematical meaning

>Thinks bait is serious

[math]
\\ \text{Continuous compounding}
\\ \displaystyle P(t)=P_{0} \, e^{rt}
\\ \text{ } P_0 \; \, \text{initial value}
\\ \text{ } r \quad \text{rate of growth}
\\ \text{ } t \quad \text{time}
\\\\
P(t_2) = 2P_0 \Rightarrow 2P_0 = P_{0} \, e^{rt_2} \\
2 = e^{rt_2} \\
e^{ln(2)} = e^{rt_2} \\
ln(2) = rt_2 \\
t_2 = \frac{ln(2)}{r} \approx \frac{70\%}{r\%}
\\
P(t_{10}) = 10P_0 \Rightarrow 10P_0 = P_{0} \, e^{rt_{10}} \\
10 = e^{rt_{10}} \\
e^{ln(10)} = e^{rt_{10}} \\
ln(10) = rt_{10} \\
t_{10} = \frac{ln(10)}{r} \approx \frac{230\%}{r\%}

[/math]

>0=1/∞
Kys

To prevent another bait, lim(x=1-)x and 0.999999........ are different number.

> lim(x=1-)x

I mean, x from lim(x=1-)x.

ex=x00!+x11!+x22!+x33!+x44!+⋯

fuck you pissbrain
mathworld.wolfram.com/Infinity.html

>informally
brainlet

big words, little grasshopper

shitposter vs W-A... we all know who's right

>"informally" is a big word
brainlet

informally isn't proof against that 1/inf= 0

read 5 lines more

Why don't you stop shifting the burden of proof and show me a framework in which "1/inf" is even well-defined.

shitposter vs W-A... we all know who's right

The WA article is of course correct but you don't understand it.

1^inf is indeterminate just like 0/0 and can equal any number

wolframalpha.com/input/?i=1^infinity

funny tho, the limit is 1

why is the limit not the value?

because infinity isn't a number
do you know the definition of a limit?

>because infinity isn't a number
...and yet it works just fine with e

If by 1^inf you mean the limit of f(x) = 1^x as x approaches infinity, then that limit is 1.

However, there are plenty of other functions in which the base converges to 1 and the exponent converges to infinity. The limits of these functions could be any number or not exist so 1^inf is indeterminate.

If we are talking about arithmetic of real or complex numbers, those are maps a : R x R -> R or a : C x C -> C. Infinity is not an element of R or C, so any arithmetic with infinity is not defined.

You mean to tell me [math]e^{\infty}[/math] is defined?

[math] \displaystyle
e = \lim_{x \to \infty} \left ( 1+ \frac{1}{x} \right )^x
[/math]

having the limit go to inf
doesn't blow up the value of e

so why does
having the limit go to inf
blow up the value of 1^x ?

nevermind, see the path towards the "1" forming is important
I just thought that 1 being a constant would calm down the situation

It's infinity. Or, to be exact, the limit of e^x for x going to infinity equals infinity

how do I into TeX?

As pointed out, [math]\infty[/math] is not a valid argument for a function [math]f: \mathbb{R} \longrightarrow \mathbb{R}[/math].
Writing [math]e^{\infty}[/math] is abuse of notation.

+ , - , * , and ^ eat 2 reals to produce a third so we write R x R -> R where the domain is the Cartesian product of R and R. If we include the "inverses" / and roots we have to be a bit more refined because they have different domains (R x R/0 and R+ respectively) and roots are multi-valued with different co-domains for each root.

It is indeterminate for the same reason as 1^inf.

Exactly. Rates of convergence are the essence of limits.

[math] x \mapsto e^x [/math] is a mapping from [math]\mathbb{R}[/math] to [math]\mathbb{R}[/math].

>[math]0=\frac{1}{\infty}[/math]
lmao

Infinity isn't a number you mongo
1/inf isn't defining anything

1 - 1 = 1/inf
1 = 1/inf + 1
1 * inf = 1 + 1 * inf
0 = 1

and that's how the Big Bang happened, QED

>autistic screeching
yeah go fight it out with WA, come back when you've won
until then I'll use 1/inf=0 in everything possible, works like a charm, erry time

You seem to be under the impression that what user is saying conflicts with what WA is saying. It doesn't.

user and Wolfram are both correct here. If that seems contradictory to you, it's because your understanding of Wolfram is incorrect.

>It is indeterminate for the same reason as 1^inf.
Nope. 1^x when x is finite is 1. e^x is not e

>multiplying with infinity
>dividing by 0
lmoa

i dont think you understand what a limit is

the limit is 1
the value is undefined

>finite number to the power of a finite number
>limit

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use the link, retard

Use your brain

I did, it told me to use the link

Get a new one then

>into TeX

look at the upper right hand corner of the textbox and find the button labeled "TeX" you may then use the tags [math and [eqn (close-bracket omitted for both or it will vanish in the post)

awww, it's retarded

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e time 2 = 200 factorial plus...?

The better equation is e^dx = (1+dx)^x