Science Forums 2

[Nootropic]

Do you not realize that if multiplication by 1, in, say the real numbers, results in division by zero then let x be a nonzero real number (note this is is also finite because we are not working in the "extended real number system" [ie. the closure of the real numbers]) x = 1*x = x/0 (which is again, not defined). And then by the density of the rationals in the real numbers, we have some sequence of rational numbers converging to x. So basically what this is saying is that NO sequence of rationals converges to any real number and density can be proven use elementary properties of the real numbers without resorting to topology. So basically this apparent "discovery" contradicts the entire field of real analysis. Now what is correct: Some "amazing" discovery or a field built upon almost 200 years of solid foundation?

If we are talking about division rings with an identity (unity), then how exactly do we deal with division by zero? This would make division rings (and hence fields) virtually unusable. Personally, I find that you have an extremely disturbed view of what the term "variable" means, how mathematics is done, and mathematics in general.

You really don't realize that such a discovery attempts to invalidate numerous fields of study. It basically makes the real analysis classes undergraduates and graduates take each year useless, because apparently the entire field of real numbers is unusable. One sign of crackpot mathematics is its implications and you fail to realize the implications your apparent discovery imposes.