Comment by gerdesj
1 year ago
There are multiple things that we denote using a particular symbol: 1. 1 in and of itself is not a single concept. You could replace the symbol 1 with any other, even the sound of a fart and the concepts still remain the same. Given that we somehow agree that a fart sound shall be the way that we refer to a concept/object/thing.
It's a largely useful conceit to use 1 for all of those objects and more besides. It makes talking about them easier but we do have to be careful to use the correct rule-set for their manipulation.
I would personally prefer to see 1.0 for "rational 1" or perhaps 1. but that would require a convoluted sentence to avoid 1. being at the end of the sentence, unless we allow for: 1.! Well, that would work but what about 1.? Oh for ffs, I mean: 1..
One notes that one's own ones may not be the same as one's other ones.
If only I could spin "won", "own" and perhaps "wan" into that last sentence! ... Right, I've wedged in own. Needs some work 8)
Well, you give give 1.0 for the rational one. But what about the real or complex one? Or what about the Gaussian Integer? What about the 2-adic one, or the 3-adic one, or any other p-adic one? What about the different kinds of floating point numbers?
I don't think the rational one is special enough that we need to different notation just for her and for her alone. (Though that specific distinction can make sense in some contexts. Just not universally.)