Mathematical Numbers (numbers used in mathematical expressions; ie. 2x+9=8y) are impossible. For example, there are an infinite amount of numbers between 0 (nothing) and 1 (a whole). If 1 is impossible to reach, then it is only theoretical, not proven.

But, I have a problem with my statement: Real-Life Numbers can be used as Mathematical numbers, and mathematical operations can be used to manipulate Real-Life numbers.

Example of Real Life Numbers: There are two eggs on a table. It's pretty obvious that there are two eggs: Therefore, Real-Life numbers are already proven to exist. But mathematical numbers are only theoretical. You can't have 1.333... eggs.

So, most of us in maths class do problems like:
Graph 2x^2+4=y...blah blah blah. Why does that work? Is mathematics only a theory, because real maths numbers are only theory? Or, maybe we use real life numbers instead of mathematical numbers, but use them as a maths medium?

More on the impossibility of maths numbers: 0.3333... is possible. It exists. 1/3 = 0.333... It is a number made from a simple expression. Any rational number can be expressed this way. So, what about irrational numbers? They can be expressed in basic maths as well. So all numbers between 0-0.999... can be proven. But, you will never reach 1, or 2, or 3. There are an infinite amount of numbers between them. That's confusing for me; if the numbers exist, and are proven to exist, then why are they impossible when put together as a whole? 1+ is only theoretical, but it is made up of an infinite amount of numbers, and each one can be proven. I don't get it.


Summary:
1. Maths numbers are theoretical; in maths expressions, we use Real Life numbers. We don't use maths numbers, because the only maths numbers, the only non theoretical numbers, are between 0-0.999...
2. WTF why can we prove each number between 0-0.999... exists, but we can't prove that 1 exists?

My conclusion for 2: 0.999... MUST be equal to 1, in order to prove that maths numbers are not theoretical; and the same onward. Ie. 2.999...3.999... etc.


What are your thoughts?