Thread: Proof - A is Infinite

I know that to prove A is finite, I say:

a bijection

So to prove A is infinite would I say:

a bijection

Our professor just said "not finite." So I am a little confused as to what to negate.

Originally Posted by Pi R Squared

I know that to prove A is finite, I say:
a bijection

So to prove A is infinite would I say:

Show that then is not a bijection.

That is is infininte if it is not finite.
does not biject with any .

Originally Posted by Plato

Show that then is not a bijection.

That is is infininte if it is not finite.
does not biject with any .

I am understanding this a little, but still not enough to prove it. This is the problem I am working on:

Proof: Suppose for the sake of obtaining a contradiction that if C is an infinite set then D is not an infinite set or \rightarrow C" alt="g \rightarrow C" /> is not one-to-one.

I clearly see the logic. But am confused as to how to relate to \rightarrow C" alt="g \rightarrow C" />.

I guess I am confused as to how can be infinite...

Originally Posted by Pi R Squared

I guess I am confused as to how can be infinite...

You really need to get this clear in your brain.
There very basis of this approach to finite set is that the set is finite.
That means that by definition cannot be infinite.

Originally Posted by Plato

You really need to get this clear in your brain.
There very basis of this approach to finite set is that the set is finite.
That means that by definition cannot be infinite.

I understand...

[tex]N_k[\math] is finite.

So I am going to have to prove that if C is an infinite set then D is not, therefore proving by contradiction that the statement is true.

I wonder if you could clarify this statement using onto and/or 1-1.

Originally Posted by Plato

does not biject with any .