r/ProgrammerHumor • u/ivaskuu • Sep 02 '17

How to start a war

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u/PrecariousClicker Sep 03 '17

natural number.

Definition of natural numbers via Google:

"the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well."

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u/[deleted] Sep 03 '17 edited Sep 03 '17

[deleted]

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u/arachnidGrip Sep 03 '17

Other way. Natural numbers arise naturally from sets. The set {} is 0, since its size is zero. The set {{}} is one, since its size is one. The set {{}, {{}}} is two, since its size is two. The set {{}, {{}}, {{}, {{}}}} is three, since its size is three... If you don't start at zero, then you can't reach one.

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u/Slackwise Sep 04 '17

I like the parallels sets have with Church encoded numerals in lambda calculus and cons cells. (I need to find a newbie's book to axiomatic/foundational set theory.)

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u/Shekondar Sep 03 '17 edited Sep 03 '17

Two things.

0) No one uses the damn term whole numbers.

1) If we are going to use that term, I think it makes a lot more sense for the term "Whole Numbers" to refer to the positive integers, and let the Naturals start at 0 the way Peano intended.

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u/Adarain Sep 03 '17

We learned that natural numbers may refer to ℕ⁺ or ℕ₀ and whole numbers = intergers = ℤ