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Math Analysis Problem.

H

Hoeboy

Banned
I need to prove that the set of Natural numbers is equivalent to the set of Rational Numbers. Basically I have to think of a function where the input is a rational number and the output will be a Natural number. This function has to be bijective. Can anybody think of one?
 
Generally this proof is done by creating a table with columns and rows counted by the integers. By starting at the 1,1 position you can follow a path on the diagonal which will pass through each cell. Not sure how to discribe this as a general function

we have f(1) = (1,1) ; F(2)= (1,2). f(3)=(2,1); f(4)=(3,1); f(5)= (2,2); f(6) = (1,3) etc,

Perhaps you can stare at that for awhile and piece together a usable relationship. Hopr this is of some help.
 
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