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Topic: A function is about ONE relation, NOT many PIECES like your
dysfunctional brains!

Replies: 2   Last Post: Nov 11, 2017 11:57 AM

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zelos.malum@gmail.com

Posts: 837
Registered: 9/18/17
Re: A function is about ONE relation, NOT many PIECES like your
dysfunctional brains!

Posted: Nov 11, 2017 11:54 AM
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>Your VERY OWN MORONICA states this!!! Chuckle. For once it is correct.

Except you are not understanding it correctly. You may want to read
https://en.wikipedia.org/wiki/Binary_relation

>In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A^2 = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms correspondence, dyadic relation and 2-place relation are synonyms for binary relation.

It says that a relation is just a subset of a cartesian product of two sets. And by Axiom schema of specification we can acquire any subset of those sets as long as we can write a predicate for it.

So when we write for example

/ x/2: x is even
f(x) = |
\ (x-1)/2: x is odd

what we are saying is that the relation/set f is defined as follows

f = { (a,b) e ZxZ: En:(a=2n & b=n) or (a=2n+1 & b=n) }

And by ZFC we are garantueed it exists and that is ONE relation as it has ONE predicate in it and by definition of relations, functions and by the axioms of ZFC, we are garantueed it exists. It is just that the former notation is much more friendly to human reading, the latter is more rigorous and exact but it is understood to mean from the former.




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