IIDB Archive

I fail to see why. You say you do not accept the law of the excluded middle. I was simply trying to make sense of this claim, to understand what it would be like if the law of the excluded middle were false, in the domain of the natural numbers. I cannot speak for cpollet, but there is at least one...

Santa's LH: I guess I was trying to say that it seems to me like the Law of Excluded Middle holds throughout mathematics, i.e. given any mathematical wff X, it must be the case that either 'X' is true or 'not X' is true. If this is wrong I would be very interested to hear more about it. So..... any...

Well, to me, .999... is a string with an unspecified number of 9s at the end. The standard interpretation of the string ".999..." is the sum as n goes from 1 to infinity of 9*(10)^-n. Since you claim you have studied analysis, you should know that the sum of an infinite series is the limi...

I'd say a set that is not enumerable should not have a universal quantifier placed on it since there is no (even ideal) procedure which could either implement the set, or check the quantifier. I fail to see why that matters. If we can pick some arbitrary member of the set and show that it satisfies...

I suppose you can get arbitrarily close (within specified precision) of 1 by using .999... or .FFFF(hex) etc. but getting arbitrarily close is not sufficient in the Doron world. No. You can get arbitrarily close by using some finite number of 9's after the decimal point. But .999... is not arbitrar...

The statement is not type-safe since it involves a universal quantifier over an (uncountably in this case) infinite set (e>0). Please define "type-safe" and explain how it presents a problem for the formal definition of a limit. I suspect you mean something like typing from computer scien...

What follows is the canonical definition of a limit: Let the function f : R -> R . We will say that the limit of f (x) as x approaches a exists, if for all e >0 there exists some d >0 such that whenever we have |x- a |< d , it follows that | f (x)- f (a)|< e . Can anyone prove that there is somethi...

Keep in mind that Doron has called Moshe Klein who is a kindergarten teacher with a bachelor's degree in mathematics a "professional mathematician". So he obviously has a very strange idea of what it means to be a mathematician.

premjan wrote: Plus only some proofs would be expected to change vis-a-vis standard maths anyhow. I don't believe Fermat's little theorem impacts any of his key concepts so the proof would not change significantly.

You've got this backwards.

I remembererd reading that the hyperreals formed a field. I know even less about the surreals than the hyperreals and assumed they did also. Thanks for the correction. It's a subtle but imo important distinction. The surreals have all of the properties one would expect in a field, they just aren't ...