Memes related to mathematics.
Rules:
1: Memes must be related to mathematics in some way.
2: No bigotry of any kind.
Theorem - All numbers are interesting
Demonstration:
By induction, all numbers are interesting
My favorite version of this proof:
Let S be the subset of natural numbers that are not interesting. Suppose by way of contradiction that S is inhabited. Then by the well ordering principle of natural numbers, there is a least such element, s in S. In virtue of being the least non interesting number, s is in fact interesting. Hence s is not in S. Since s is in S and not in S, we have derived a contradiction. Therefore our assumption that S is inhabited must be false. Thus S is empty and there are no non interesting numbers.
Counterproof:
n+1 is not the smallest non-interesting number... n-1 is.
What about 31? That's the smallest non-interesting number so if we take that as the first n, then every n+1 is either interesting or the second-smallest non-interesting number, and the second smallest non-interesting number is still not interesting.
31 is prime, that's interesting isn't it?
what about the real, non-rational numbers?
I think 6 is a rather big number. It’s more than I can count on one hand.
Start counting in binary. Gets you to 31 on one hand, 1023 on two.
Chernobyl math
I've seen smaller 😏
I don't think you can induce all numbers from n+1
True, You can only induce natural numbers from this.
However, you could extend it to the positive reals by saying [0,1) is a small number. And building induction on all of those.
You could cover negative and even complex numbers if “small” is a reference to magnitude of a vector, but that is a slippery slope…
In a very not rigorous way, you can cover combinations of ordinal numbers and even non-numbers if you treat them as orthogonal “unit vectors” and the composite “number” as a vector in an infinite vector space which again allows you to specify smallness as a reference to magnitude like we did for the complex numbers.
If you multiply two not really numbers, just count the product as a new dimension for the vector. Same with exponentiation. Same with non math shit like a cow or the color orange. Count all unique things as a unique dimension to a vector then by our little vector magnitude hack, everything is a small number, even things that aren’t numbers. QED.
This proof is a joke, broken in many ways, but the most interesting is the question of if you can actually have a vector with an uncountably infinite (or higher ordinals) of dimensions and what the hell that even means.
Sure you can. Proof:
0 is a number.
If n is a number, n+1 is also a number.
Therefore, by mathematical induction, we can induce all numbers.
☝🏽🤓 The naturals are hardly all numbers, considering they're only a countably infinite subset of the reals.
Weird. There are no numbers that can't be added. I wanted that.
But what abut 10⁸⁰ + 1 ??
This is a poor definition, a small number is usually defined by an inequality.