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Search found 1221 matches
 Mon Aug 22, 2005 3:55 pm
 Forum: Philosophy
 Topic: Law of Excluded Middle
 Replies: 97
 Views: 1482
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...
 Sun Aug 21, 2005 7:42 am
 Forum: Philosophy
 Topic: Law of Excluded Middle
 Replies: 97
 Views: 1482
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...
 Wed Aug 17, 2005 2:46 pm
 Forum: Philosophy
 Topic: The opposite of Emptiness
 Replies: 114
 Views: 1463
 Wed Aug 17, 2005 1:05 pm
 Forum: Philosophy
 Topic: Limits
 Replies: 35
 Views: 522
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...
 Wed Aug 17, 2005 12:57 pm
 Forum: Philosophy
 Topic: The opposite of Emptiness
 Replies: 114
 Views: 1463
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...
 Wed Aug 17, 2005 7:06 am
 Forum: Philosophy
 Topic: Limits
 Replies: 35
 Views: 522
 Wed Aug 17, 2005 7:04 am
 Forum: Philosophy
 Topic: Limits
 Replies: 35
 Views: 522
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...
 Sat Aug 13, 2005 7:04 pm
 Forum: Philosophy
 Topic: Another Challenge for Doron
 Replies: 55
 Views: 765
 Wed Aug 10, 2005 6:23 pm
 Forum: Philosophy
 Topic: A Mathematical Challenge for Doron Shadmi
 Replies: 75
 Views: 1533
 Tue Aug 09, 2005 9:35 pm
 Forum: Philosophy
 Topic: Super position and a free will
 Replies: 383
 Views: 4128
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 ...