Partial Recursive Functions 2: The basic functions

[@owenbraun3390]

Hey, what happens if you put a 0 into a zero1 function? would it be 1 since 0^0 is 1?

[@AsaNole]

Great videos! What textbook can I use to supplement?

[@BelegaerTheGreat]

Just a note, the zero and succ functions can themselves be defined by Peano.

[@lakshaysagarrana3965]

In successor function, How the range is Natural Number? Since nothing in domain would result in Zero. Please explain.

[@lakshaysagarrana3965]

Or one could say the it is partial function ?

[@HackersatCambridge]

You are right that no possible input would result in an output of 0. Of course, every output is a *member* of the natural numbers (hence the natural numbers are a valid choice for the codomain here) but that's not to say that every member of the natural numbers is a possible output of the function. We could define a more precise codomain that did not contain 0 but that's not particularly more useful here. We sometimes distinguish between the *codomain* (as, roughly, 'the things that might come out of this function') and the *image* (as, roughly, 'the things that actually do come out of the function for some input'). This is not an important distinction for this video series. Note that the fact that 0 is not a possible output does *not* make this a partial function. A partial function is one for which the output is undefined for a particular *input*.

[@lakshaysagarrana3965]

Hackers at Cambridge thnkuu

[@abdelkrimnachef352]

thx a lot

[@xnopyt647]

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