jayjacobus wrote: ↑Tue Nov 17, 2020 1:39 pm
Numbers are a frame of reference for amounts.

amount = quantity

Without numbers amounts are imprecise.

You mean, if you didn't know numbers, three goats might really be four goats, or two and half goats, and you couldn't tell?

No, I'm pretty sure that amounts/quantities were the same before humans named them and will still be same when humans are extinct.

Using numbers in a sentence is an example, not a definition.

Unless the sentence is a definition, i.e. : A number

**is **a verbal symbol for a quantity. A numeral

**is** a visual symbol for a quantity. Mathematical signs are visual representations (symbols) of mathematical operations that express interactions and relationships between quantities. The verbal counterpart of these symbols are 'plus' 'times' 'square root', etc.

Saying that numbers are words, which are symbols, is not a definition because all words are symbols, not just numbers.

I already said that. Words are verbal symbols for real things, places, persons, processes, relationships and ideas. The numbers are the words we use for quantities.

A mathematician uses numbers in geometry, algebra. calculus, etc. but without a way to specify amounts each subject would be meaningless.

This is absolutely true. Also true: if humans had not invented the language of mathematics, there could be no disciplines of algebra, geometry, calculus, etc. And then where would the mathematicians be, eh? They might have to go herd goats and never be quite sure how many they had.