# Bijection and set

1. Mar 2, 2010

### jihyel

How can I show an explicit bijection between sets?
anyidea?

Last edited: Mar 2, 2010
2. Mar 3, 2010

### CompuChip

You just write down a function. Do you know what the definition bijection is?

For example, if you want to show a bijection between A = {0, 1, 2, 3, 4} and B = {8, 9, 10, 11, 12} you could write
$$f: A \to B, f(a) = a + 8$$
(for finite sets, you can also write it out as: define f by f(0) = 8, f(1) = 9, ..., f(4) = 12).

How about it? If you mean: how about a bijection, you are asking half a question. A bijection is always between two sets. "How about a bijection from (0, 1) to (3, 4)", or "from (0, 1) to (0, 1)", or "between (0, 1) and (-2, 2)" would make sense.

3. Oct 26, 2010

### nando09

Compuchip is correct. Think over it.