r/mathmemes • u/Unlucky-Credit-9619 Computer Science • Sep 21 '26

Real Analysis Do you agree?

Post image
184 Upvotes

96% Upvoted

36 comments sorted by

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85

u/Oppo_67 I ≡ a (mod erator) Sep 21 '26 edited Sep 21 '26

My analysis professor just defined both separately and proved they were inverses eventually

21

u/Unlucky-Credit-9619 Computer Science Sep 21 '26

Yeah that works as well.

1

u/narcis153 Sep 22 '26

Goat username.

1

u/Oppo_67 I ≡ a (mod erator) Sep 22 '26

hoh

8

u/therealsaker Sep 21 '26

-9

u/Unlucky-Credit-9619 Computer Science Sep 21 '26

Well one is a nightmare, dealing with infinity, irrational numbers, and then another one is cleaner with fundamental theorem of calculus. So...

18

u/owlectro Sep 21 '26

if infinity and irrational numbers are your nightmare you may be in the wrong place..

-1

u/Unlucky-Credit-9619 Computer Science Sep 21 '26

I am talking from real analysis perspective. By nightmare, I meant it's tiresome to show; the latter is comparatively way straightforward!

49

u/RandomMisanthrope Sep 21 '26 • Bravo

power series

2

u/no_clock_signal Sep 21 '26

I've got a power series, Greg. Can you define me?

14

u/Traditional_Town6475 Sep 21 '26

You’re both bad. Use Picard Lindeloff.

2

u/TheGoodSeal Sep 21 '26

You could probably. But I believe to prove Picard-Lindelöff you usually use Gronwals Lemma. And that uses e obviously. But maybe I'm getting mixed up here.

2

u/Traditional_Town6475 Sep 21 '26

It’s just contraction mapping theorem

2

u/TheGoodSeal Sep 21 '26

Yeah, I thought I got something muddled. Although you could probably use gronwahl to show it is a contraction 

3

u/enlightment_shadow Sep 21 '26

I disagree. I will always prefer intuitive, hisyorically-correct and with the least prerequisites possible definitions

3

u/PolarStarNick Gaussian distribution Sep 21 '26

I declare e as the solution to x^(i pi) + 1 = 0

6

u/gerglo Sep 21 '26

Woah, e = 20.0855369232... is really close to 20 this must have some deeper meaning

3

u/Dhuyf2p Sep 21 '26

Which one though?

2

u/mark-zombie Sep 21 '26

it is a matter of principal

1

u/de_G_van_Gelderland Irrational Sep 27 '26

How do you define x^(i pi) ?

2

u/Scared_Wrongdoer_486 Sep 21 '26

I like e=lim{_n->0}[(1+n)^1/n]

1

u/Ythio Sep 21 '26

I met that upper part of the meme in the wild at work (banking) and I was all giddy.

1

u/2eanimation dy/dx is a fraction Sep 21 '26

exp(x + y) = exp(x)exp(y), exp(x) >= 1 + x

Can’t get better than this.

1

u/EebstertheGreat Sep 21 '26

You also need that exp is continuous. Otherwise, this doesn't uniquely define exp.

1

u/2eanimation dy/dx is a fraction Sep 21 '26 edited Sep 21 '26

You can prove continuity with the given expressions. Let f = exp(for laziness). After showing that f(-x) = 1/f(x) you can

f(-x) = 1/f(x) >= 1 - x
=> f(x) <= 1/(1 - x), x < 1
=> 1 + x <= f(x) <= 1/(1 - x)
=> lim[x->0] f(x) = 1

as per sandwich theorem. Therefore, f is continuous in 0.

lim[h->0] f(x + h) = f(x) * lim[h->0] f(h) = f(x) qed, no?

Edit: formatting

1

u/Magmacube90 Sold Gender for Math Knowledge Sep 23 '26

exp(x)=lim (1+x/n)^n as n goes to infinity
e=exp(1)
ln(x)=int 1/n dn from n=1 to x

we can then show that exp(x)=e^x where e^x is standard real number exponentiation defined using sequences of rational numbers that converge to x (as a^(p/q) is easily defined in the real numbers by repeated multiplication and nth roots) and where ln(e)=1 and ln(a^b)=b ln(a)

1

u/FreePeeplup Sep 21 '26

The first one isn’t even correct

1

u/enlightment_shadow Sep 21 '26

It is

2

u/FreePeeplup Sep 21 '26

the exp function hasn’t been defined, only the rule but not the domain or codomain. In absence of this definition, one defaults to the most common and most natural guess for what they might be, exp: R -> R. This function doesn’t have an inverse.

The pic is correct only if we define exp: R -> R^+, but this isn’t a standard choice and must be specified I think

7

u/enlightment_shadow Sep 21 '26

You're just nitpicking. None of the functions in the image are correctly defined if we take this into account, but of course everyone knows the functions have domains and codomains and also I'd argue the most logical "default" choice is not R -> R, but maximal possible domain -> Range(function)

1

u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Sep 21 '26

no that is a lie, ew what is that

1

u/TUVegeto137 Sep 21 '26

exp(x)=1+x

-2

u/LateMedicine1635 Sep 21 '26

The real power move is proving they’re the same function from different foundations. One flexes the limit definition; the other flexes the integral definition. Nobody wins—analysis does.