What does the term 'unequal' mean if there is no prior assumption of it?

Q: What does the term 'unequal' mean if there is no prior assumption of it? A: Just use the definition of the limit of a sequence to understand infinite proximity, just like taking a ruler, no matter what ruler you take out, these two things are the same size.

Infinite proximity is equality on many meaningful scales.

For example, if I use the ruler of natural numbers to measure, 1 and 1.1 are the same thing, and 2 and 1.1 may also be the same thing, then other natural numbers are definitely not the same thing, that is, "not equal".

If measured with the ruler of fractions, 1 and 1.1 are no longer the same thing, but a small real number can still be added to make 1.1 the same under the ruler of fractions.

Most of the time, infinite proximity requires us to measure with the ruler of real numbers, which is the same. Of course, there are also numbers larger than real numbers, which correspond to more abstract rulers.