What is a binary operation?

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[wojteksocha]

"0 is not a natural number"
And I took it personally

[fbkintanar]

"Zero is not a natural number." Don't tell that to a computer scientist, for us zero is always part of the natural numbers. Programmers even start indexing arrays and sequences with zero, and models of computation use a logician's method of constructing the natural numbers (Peano arithmetic) from the constant zero and the function successor(). Mathematicians should do that to. Monoids are more natural than semigroups, just ask a category theorist.

[TranquilSeaOfMath]

An example of an Unary operation is the factorial on the natural numbers. This operation requires only one element from a set to perform a calculation. After hearing binary operations mentioned so much; I had wondered about operations that were not binary.

[tinkeringtim]

I wish binary operations were called 2:1 reduction operations. Binary should be kept for either reversible two variable gates, or for a genuinely binary irreverable gate which outputs (1, C) forall Bin(A, B). The latter may seem like a trivial technicality, but in terms of formalism it's quite different.

[jorgesaxon]

Are there any ternary operators that cannot be defined by a composition of binary operators?

[MochiClips]

In my groups class in first year they also explicitly added the condition the operation has to be closed

On sexond look you've done that quite subtly by having *:AxA->A (output ends up back in A) clever!

[vincentbutton]

Lol! When the teacher throws in a ringer and we forget what the lesson was about. Go ZERO!!!

[joefuentes]

Why do some people say 0 is a natural number and some don't? I've tried to Google it before with little satisfaction. I normally like to see natural numbers not include zero and the set with natural numbers and 0 be defined as the "whole numbers" using the fancy W... Alas...

[chrissquarefan]

Why is 0 not natural? I've always been taught of N containing 0. N* on the other hand has no 0.

[florisv]

That's a very abstract definition that may well be too difficult for the people who ask the question about what binary operators are in the first place.

[ReCaptchaHeinz]

0 is not a natural?? 🥺🥺🥺 I mean, I get Pluto not being a planet, but what did zero to get kicked out? :(

[youtubepooppismo]

isnt that more of a homogeneous relation

[Peibolia]

Maybe it is you who's not a natural number.

[GKinWor]

NO come on man plz let 0 into the club its pluto all over again

[cd-zwtt]

2 has no multiplicative inverse my ass. 1/2? Someone please explain why that doesn't work.

[mcqueen]

Saying 0 is not a natural number: cringe. Defining binary operation as having to output back into the set A instead of another set: mega cringe.