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/sci/ - Science & Math

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5652884 No.5652884[DELETED]  [Reply] [Original]

It has recently come to my attention that there are people on the internet who do not believe that any proof by induction can ever be valid... They're cranks right?

>> No.5652897
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5652897

induction isn't proving anything, it's assuming what you are supposed to be proving. It's still useful in many practical applications, but it's the lazy man's proof, for when they cannot get to the real underlying truth of the matter, which unfortunately is the case often. A perfect logician understands infinite inductive cases is not concrete and leaves an unbounded patch to a problem that may or may not be able to be put not finite structure. Are there problems which are unsolvable without induction in the universe? We just don't know. But if there is than the universe is truly a weird place.

>> No.5652898

>>5652884
I had a potato, it was brown, it was also in a brown sac, the potato is thus a sac

QED

>> No.5652900
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5652900

If any Nth case and Nth+1 case holds true then you'll have a hard time finding a counter example for any N value within the given parameters.

>> No.5652903
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5652903

>>5652900
Any time I take a step forward, I am one step further from where i started. It seems to hold true until you end up where you started.

>> No.5652905

>>5652897

wow you know nothing about induction

"assuming what you are supposed to be proving"

fucking idiot lol,

you don't assume what you are proving... you assume P(k) then derive P(k+1), thus proving the general if-then sentence: if P(k) then P(k+1)

now having proved if P(k) then P(k+1) the base case P(a) now implies P(a+1), but P(a+1) implies P(a+2), but P(a+2) implies P(a+3) and so on...

>> No.5652912

You fucks know nothing past high-school level induction.

Hint: Real mathematicians don't try to prove the (k+1)th case. We prove that every case from base case to (k-1) holds.

>> No.5652917

>>5652912
Your second statement follows from the principle of induction.

>> No.5652943

>>5652905
That's the thing with induction. You don't make assumptions.

But that's how deduction works. Assumptions everywhere.

>> No.5652949

>>5652912
>We prove that every case from base case to (k-1) holds.
I think you mean "assume".

>> No.5652953

We don't directly prove that the n+1th case holds. We prove that it holds for SOME n, not EVERY n. We make the assumption that it holds for SOME n, and then we show that if it holds for SOME n, then it holds for n+1.

The second part of the proof is just finding SOME n, the base case.

People don't believe induction works because they think we're making the assumption for EVERY n. They fail to see the nuance in the keyword "some", which makes all the difference.

>> No.5652957

When the singularity arrives we will not need to rely on induction because we will be able to actually test every number up to the largest one.

problem echoron?

>> No.5652960

ITT: People not knowing the difference between logical and mathematical induction.

Mathematical induction is fine
Its logical induction that is fucked

>> No.5652974

It has recently come to my attention that there are people on the internet who do not believe that any proof by induction up to <span class="math">epsilon_0[/spoiler] can be valid... They're cranks right?

>> No.5652997
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5652997

It has recently come to my attention that there are people on the internet who do not believe infinite sets can ever exist mathematically... They're cranks right?

>> No.5653012
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5653012

>>5652884
Well, if they are nobheads and don't believe in the amazing power of induction. Then let those bastards dis-prove by contradiction instead; those winging plebs

>> No.5653046

>>5652884
It has recently come to my attention that there are people on the internet who do not understand Mathematical Induction... They're cranks right?

"A way to establish the truth of a statement about all the natural numbers or,sometimes, all sufficiently larger integers". - Discrete Mathematics with Graph Theory

>> No.5653051

>>5653012
M- M- RGB RGB

>> No.5653058

>>5652903
and hence the proof fails.

Proof by induction is perfectly valid, if you do it right.

No point in discussion: Find a proof by induction(which is held to be true) and a counterexample please