3 ms·

So from that point of view, where the real numbers exist in the same way infinity exists -- they're not really numbers but ideas about numbers. Pi isn't a numb

• Retra 8y ago
  They can be numbers and abstractions. There's not really any definitive singular notion of what a number is, so it wouldn't be very useful to say something like pi isn't a number. (If you can do arithmetic on it, chances are it is a number, regardless of what else it represents)
• Koshkin 8y ago
  Indeed, numbers are abstractions. Even the number ‘5’ is an abstraction, let alone the numbers that cannot even be measured precisely - not even in principle. >idea about a circle As if a circle is a real thing. (Circles do not exist, either - or, rather, they ‘exist’ in a very particular sense of the word, as they are themselves abstractions; round things do.)
  • sevensor 8y ago
    > As if a circle is a real thing. (Circles do not exist, either - or, rather, they ‘exist’ in a very particular sense of the word, as they are themselves abstractions; round things do.) Well, yes, exactly. The thing that intrigues me about this discussion is that it seems like mathematicians have a much clearer idea than I do about what the differences between these kinds of abstractions are.