ITT bijections from the reals to the non-zero reals. I'm stumped.
Name:
Anonymous2007-06-04 21:06 ID:YBDeww2/
Got one:
f(x): R -> R*
_
/
| x -> 1/(x+1) , x < -1
f(x) = <
| x -> x + 1 , x > -1
\_
Name:
Anonymous2007-06-04 21:07 ID:YBDeww2/
fuck. (undefined for -1). back to the old drawing board.
Name:
Anonymous2007-06-04 21:09 ID:9+ZlAEDs
>>1
Let {a_n} be a sequence of non-zero real numbers. Define the function f(x) as follows: if x = 0, f(x) = a_1. If x = a_i, f(x) = a_(i+1). Otherwise, f(x) = x.
Name:
Anonymous2007-06-04 21:17 ID:Q7zn7vT6
x -> x, x not integer
x -> x + 1, x integer less than -1
x -> x + 2, x integer greater than or equal to -1