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Uhm, anything that is part of a definition follows from that definition. `A and B implies A' and so on. In the end a function, in the mathematical sense, is j
by thomasahle 13y ago
Uhm, anything that is part of a definition follows from that definition.
`A and B implies A' and so on.
In the end a function, in the mathematical sense, is just a long (possibly infinite) table of `from' and `to' values. We could argue that one definition of ^ is more or less complex than another, for some definition of complexity, but I'm not sure which would win, and if it would be useful.
- pavelrub 13y ago"Follows" in the sense that it is not an axiom - it has a proof of more than one line in the sense of the Hilbert system. Seeing functions as collections of ordered pairs tells us nothing here. Your definition of ^ doesn't directly tell me that 2^1=2. It does tell me however that 0^0=1.