On: Does mathematics need a philosophy?

[Koshkin]

Indeed, the Avogadro number is an integer that is always given in the form of a floating point number. The reals is such a useful abstraction.

[burnished → Koshkin]

No, it is typically described using scientific notation - floating point is a fixed width representation of a number with fractional parts.

[jameshart → burnished]

And floating point numbers - and scientific notation - can both only express rationals. They aren’t ‘reals’.

[Koshkin → jameshart]

My point was that it seems that in calculations it is useful to think of very large integers that are known to some approximation as real numbers.