# Real Numbers

If we were to take any two integers on a real number line and mark a point (a number) halfway between the two, do the same in the range between the halfway point and each of the two numbers, and continue the process, would we be able to define all real numbers between the two integers (including irrational numbers) as the limit of a rational expression or a series of rational expressions?

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Guest
I think not. Because whatever you define would not be countable.

Office_Shredder
Staff Emeritus