Re: Contradicrtion-free mathemattics (The new nonstandard analysis
I will define it in terms of "decimals" in any base greater than one:
Liebniz's infinitessimal is a one in the infinitieth place,
preceded by a nonterminating series of zeroes
(to the right of the "point").
if you subtract this from one,
you get 0.9999..., period!
-------------
Actually, "infinitieth place" is ill-defined because you cannot reach it.
Then how can you subtract that infinitesimal from 1?
One cannot add, subtract or multiply nonterminating decimals because you need a last decimal digit to do any one of them. However, one can divide by terminating decimal because division starts on the right digit of a number which is known. For example, let x = 1, y = 0.99...
then
(x+y)/2 = (1.99...)/2 = 0.99...
Aha! Who said that the average of two unequal numbers lies strictly between them?
E. E. Escultura
.
