Eckard Blumschein wrote: > Someone wrote: ... [1.5 , 2.5) > (where 1.5 and 2.5 are 'infinite-precision' numbers...) > Does nobody share my reluctance to distinguish between > included and excluded infinite-precision numbers?
Sure; cf. Hjlemslev. But perhaps it is best to dig somewhat deeper.
Let us forget, for a moment, these infinite precision numbers. Let's say, we have (or want to have) a number system that contains only your 'interval-like' numbers. So, for example, there exist numbers like 0.27 and 0.270, but these numbers are different (contrasting with the usual system). Now i suppose you may want to define some special relation between these numbers, namely something like ' 0.27 is an approximation of 0.270 ', or '0.270 is a precization of 0.27 '. Is that still along your line of thoughts?
Now, would you like to say that, eg., 0.27 approximates 0.27499 and it also approximates 0.27499999 and also 0.274999999999, etc. but that 0.27 does not approximate 0.275, nor 0.2750, etc. ?
Or do you want something more subtle than that?
> I am not Buridan's donkey.
Neither is any of us (i suppose), thank you. Can you explain what relevance you see for that old story in this discussion? What are the two things that modern mathematics fails to choose from, and what does it miss, because of that?