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0 pointszekrioca1y ago0 comments

> It is very, very simple, and I would say easier to learn than Python, as long as you remember that it is not programming but maths. For example, suppose you specify this function on the integers:

> f ≜ CHOOSE f ∈ [Int → Int] : > ∀ x ∈ Int : f[x] = -f[x]

> What function is it? Clearly, it's the zero function

Did you mean your example is the constant function [1], rather than a zero function [2] (where c = 0)?

[1] https://mathworld.wolfram.com/ConstantFunction.html

[2] https://mathworld.wolfram.com/ZeroFunction.html

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pron1y ago

I mean the zero function, i.e., the one that is zero everywhere, because if y ∈ ℤ and y = -y, then y = 0.

zekriocaOP1y ago

Doesn't ℤ include negative natural numbers?

* Nevermind, I just saw you used the ">" sign in the definition. Is it why the definition only applies to positive numbers? In any case, you did not write it in your textual description, which looked confusing to me. I think it would be easier if one could define it as ℤ+ or something like that.

Jtsummers1y ago

The original from pron:

    f ≜ CHOOSE f ∈ [Int → Int] : 
       ∀ x ∈ Int : f[x] = -f[x]

You added the > in your quote of pron, he didn't have it in the original. There is no c in ℤ with c != 0 s.t. f(x) = c and f(x) = -f(x), that would imply that c = -c for non-zero integers which is not true. The only function that can satisfy pron's constraints is f(x) = 0 since c = 0 is the only time c = -c, or 0 = -0.

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