Proof by induction

>proof by too narrow of a margin

>assume (not P) is true
>P is false, QED

>let A be some number such that this proof works

>proof by plucking some magic function out of thin air

>proof by accident

>proof by induction on a formula I pulled out my ass

>proof by "contradiction"
>is actually a very poorly formatted proof by contrapositive

>assume something
>prove your assumption wrong
vs
>prove something worded differently

>proof by numerical simulation

>proof by drawing some fucking arrows

>let

He's right though. Look at half of proofs by contradictions you see, and you'll be able to turn them into proofs by contrapositive with no effort.

>proof by unification

>proof by convenient definition

>He doesn't add a "assuming n+1 exists" to his induction proofs
It's like you don't even want to do real math

>proof by getting dubs

>reading logic textbook
>authors says some people think induction is inherently poor form, never being able to provide a decent argument
>author says some people think induction doesn't even exist
>author says we will just be dealing with deductive logic in this book
ok, i wonder why they think that

>assuming n+1 exists
What a fucking retard. You're supposed to write an algorithm, let it run for a long time and calculate the p-value.

Don't unerdstand this either. Except you are memeing with transfinite induction, there's literally no counter intuitive shit thay comes from using induction. Why take the only math CS has?

>proof by proving

>proof by exercise

Is it really a meme?

>Analysis

The only math CS really has is Calc and discrete mathematics (strictly logic based).

>proof by chadness

>proof by a contradicting induction tautology

...

>proof by intimidation

Where was this user when I was studying abstract in undergrad?

>proof by choice axiom

follows from the peano axioms, brainlet

Those anons are right though. Alot of proofs by contradiction basically work like this:

Proposition: The sum of two even numbers is even.
Proof: Assume there exist two even numbers 2a and 2b whose sum is odd. But 2a + 2b = 2(a + b) is even. Therefore an odd number is even. Contradiction.

It's trivial to reformulate that as a direct proof, but what's interesting is that there actually are proofs that you can't really reformulate. Take the proof that sqrt(2) is irrational. Try restrucuring that as a proof by contrapositive.

when somebody writes a proof which is basically a direct proof with "Assume not P" and "Therefore contradiction" tacked onto the beginning and end, it tells me they're not paying attention to what they're doing

~sqrt(2)=~a/b such to at a,b are integers implies that 10 = 20/10
QED

fuck I meant 20/2
haha funny joke I'm so funny

>Take the proof that sqrt(2) is irrational.
that's a proof of negation, not proof by contradiction ()

You can only use contrapositive when your theorem is written in the form "p implies q" and even then, you have to specifically prove "~q implies ~p", which is the same process as assuming ~q and derive a contradiction with p. That's why everyone who isn't a freshman just assumes the theorem to be false and moves on.

Proof. Behold!

literally every theorem in mathematics is in the form "p implies q"

Isn't the fact that sqrt(2) is an infinite fraction proof enough that it's irrational?

I don't follow your reasoning here. It sounds like you're saying the theorem is true because it implies a true statement.

I fucking hate this shit. Every single proof in my Functional Anal class is contrapositive yet is written like a proof by contradiction

>proof by hindsight

>what is well-ordering

>proof by triviality

I was trying to "prove" the irrationality of the sqrt(2) by using the contrapositive to imply something that's vacuously true
but I did it wrong anyway
so I did it wrong on purpose to be funny but I still fucked it up

>about to start grad school in math
>never did any homework questions or test problems that required proof by induction
they can't start making me either

> be engineer
> never done a proof in my life
> actually forgotten everything above calc 1
> people think im a math genius

kek

KEK

K-E-K

>fraction
[math]\frac{sqrt}{2}[/math]

>they can't start making me either
that's where you are wrong, kiddo

kek

It's how we keep brainlets out of math.

>assuming axiom of choice

brainlet

>things nobody says

>charge by induction

Prove each even number is followed by an odd number, and vice versa.

> well it's obviously fucking true
QED

>proof by farting

My point-set topology class in a nutshell

>proof by saying Kevin solved it

>proof: check in the pudding!

Other times when a text book makes a joke?

Linear algebra too

Let n be any number. Then n + (n+1) = 2n+1 which is odd. The sum of two evens or two odds can't be odd. qed

>proof by inadequately-sized margin

>proof by copying a classmates work
who else here /cheet/

>proof by circular reasoning

>proof by me fucking your mom

>proof by making shit up

I am pretty sure they were not talking about mathematical proofs by induction but about empirical inductions like: “Every day I have seen the sun has risen. Therefore it must rise tomorrow again”.

Why do these kinds of threads get so many replies? Is it so much to ask that only people with a genuine interest in and an aptitude for math and science post on this board? Fucking hell.

>proof by calling it trivial

Because we are on Veeky Forums.

>Proof: see lecture X class notes
zero marks every time

There are maybe 5 or 6 actually intelligent people on this board. The vast majority are undergrads or high schoolers who think their ACT scores make them a genius.

>proof

Nope.

that is not circular reasoning, brainlet

If ZFC holds, then R exists

brainlet

>i climb first step
>if i was at random step in middle of staircase, i could get to the next step
>so i can get up of whole the stiars

You're rewriting a theorem in a way that fits your preferred method for writing proofs, which is exactly what you're complaining about.

>squeeze theorem

>there's literally no counter intuitive shit thay comes from using induction
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>proof by tautological reasoning

He's right though

>proof by leaving it as an exercise for the reader.

>proof by torture
>2+2=5