Your wording is all very confusing to me. First of all, just because there are an infinite number of numbers between 0 and 1 doesn't mean you will never reach 1. There are an infinite number of numbers period. Every number exists. Saying you can't reach it because there are an infinite number of numbers in between just doesn't make sense. Also, you can add an infinite number of numbers and get a whole number.

The number 1 does exist. Its value is 1.0000000000000000000........ repeating forever. It is also equal to .999999... repeating forever. Source

Second, saying numbers are only theoretical doesn't make much sense. They aren't real, but that doesn't exactly make them theoretical. Within the realm of mathematics a number has a precise and defined value. It isn't theoretically 1, mathematically it is 1. The only reason you can't have 1.33333333333333333........ eggs is because the real world isnt infinitely divisible. In math, things are, so you could have that many eggs. Infinity doesn't exist in the real world, and I think that is what is confusing you.

I'm sorry if my response is vague or doesn't exactly address what you were saying. Your post kind of confused me and i couldn't tell exactly what you were trying to say.