Thanks MathGrrl

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Patrick may, aka MathGrrl, links to what is infinity? At the end we read:

If you continue to study this subject you will find discussions about infinite sets, and the idea of different sizes of infinity.

That subject has special names like Aleph-null (how many Natural Numbers), Aleph-one and so on, which are used to measure the sizes of sets. 

For example, there are infinitely many whole numbers {0,1,2,3,4,...},

But there are more real numbers (such as 12.308 or 1.1111115) because there are infinitely many possible variations after the decimal place as well. 

It looks like I am not so wrong after all.

And Neil Rickert says:

 People have obviously tried looking at cardinality in accordance with simple intuition. That works with finite sets. But, when tried with infinite sets, it quickly leads to logical contradiction. The way we actually handle cardinality might look unintuitive to you, but it avoids those logic contradictions.

Neil, when you can actually count the number of elements in each set then that ain't being intuitive. That is being able to do basic math. What logical contradictions are you talking about? Please list them. Thanks.