On Saturday, September 30, 2017 at 7:01:04 AM UTC-6, John Gabriel wrote:
> Well, for starters, education of calculus is in a dire mess. Students > never understand calculus. Even their professors never understand. > They simply learn to use.
Well, even if I don't agree with much of what you've said, I can certainly grant you this point...
since the ancient Greeks had so much trouble with what we call "irrational numbers", why couldn't it be the case that today's math students might have the same problem...
and thus benefit from a calculus that can work without them?
You are correct that 1/4 = 0.25 is the same as 1/4 = 25/100, too.
It may be wrong, in some sense, to say that 1/3 = 0.3333... but it is correct that 1/3 is greater than 3333/10000 and less than 3334/10000. Similar things can be said about pi - even if pi is not really a number, sometimes, like when figuring out how much adhesive tape will fit on a roll, we might want to do arithmetic with it.
However, I don't think I could get you to consider that perhaps you and conventional mathematicians are simply using different words to talk about the same thing.