archiver 8

Monday, February 20, 2006

bijections from NxN onto N

bijections from NxN onto N
tag: t math. t function. t bijection. t polynomial. t zakon.

bijections from N x N onto N
f(n,m) = 2^n (2m-1)
g(x,y) = g(s,y) = 1/2 (x+y-1)(x+y) + (1-y)

For f, observe that the expression 2m-1 usually denotes odd numbers. f comes from and gives rise to a multiplication-based decomposition of N into N pieces.

For g, consider s = x+y as fixed and y varing. g comes from and gives rise to a decomposition of N into N intervals.
In fact, g is the famous zig-zag proof of equinumeracy of N x N and N.
Note that g is a polynomial.

Note that, to prove that f and g are bijections, we find meanings in the expressions of f and g. Find meanings and motivations in expressions, formula, formulation, proof, theorem, conjecture, equalities, inequalities

ref:
f from sci.math
g from http://www.trillia.com/distr3/zakon-basic-a4-one.pdf

0 Comments:

Post a Comment

Links to this post:

Create a Link

<< Home