- #1
honestrosewater
Gold Member
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From my book:
"We agree that there is exactly one 0-tuple in [set] X, and we designate it by ( ). A 0-ary function from X to Y is then completely determined by its value for the argument ( ). We shall identify the function with this value. This means that a 0-ary function from X to Y is simply an element of Y."
I don't understand the reasoning behind the second sentence. How does a function even work on an empty sequence?
Edit: I may as well tack this on here. "universe" and "individuals" are undefined terms, right? I've never seen them defined, not formally anyway, and they seem to be basic concepts.
"We agree that there is exactly one 0-tuple in [set] X, and we designate it by ( ). A 0-ary function from X to Y is then completely determined by its value for the argument ( ). We shall identify the function with this value. This means that a 0-ary function from X to Y is simply an element of Y."
I don't understand the reasoning behind the second sentence. How does a function even work on an empty sequence?
Edit: I may as well tack this on here. "universe" and "individuals" are undefined terms, right? I've never seen them defined, not formally anyway, and they seem to be basic concepts.
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