What are the natural numbers? Is it a valid question at all? My understanding is that a set satisfying Peano axioms is called "the natural numbers" and from that one builds integers, rational numb...

From the Wikipedia article: In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers $\ {1, 2, 3, \dots\}$ according to the traditional definition; or the …

Dec 14, 2023 · The usage of the natural numbers and all the properties you know and love came first. The definition involving set theory and emptysets and such came after and was specifically …

Sep 21, 2017 · This set N N is a subset of the real numbers, and behaves (in every meaningful way) as the natural numbers— N N is isomorphic to N N. So perhaps it is reasonable to call N N the set of …

Apr 5, 2015 · Alternatively, if you were asked to define the natural numbers, you could do so axiomatically. With this method, you begin by declaring an element is a natural number, and it really …

Nov 17, 2018 · Well, as I said before, string theorists need to use the sum of all natural numbers and if they use the value−1 12 1 12 they get accurate results (is what I have heard).

Jul 5, 2019 · The ordering of the naturals is actually much easier to define if we use the set-theoretic interpretation via the axiom of infinity: the axiom of infinity guarantees the existence of the ordinal ω …

Then is there a problem with my definition? I've thought I'd defined the set X as the set of all finite subsets of the natural numbers.

You can't seriously believe there are only finitely many numbers. "If a natural is finite, then that natural plus one is finite, hence the set of all naturals is finite" - this is a non sequitor, the set of all naturals is …

Possible Duplicate: How do I come up with a function to count a pyramid of apples? Proof that ∑ k=1n k2 = n(n+1)(2n+1) 6 ∑ k = 1 n k 2 = n (n + 1) (2 n + 1) 6? Finite Sum of Power? I know that the sum …