RE: Maths proves 1=0.999.. thus ends in self contradiction

December 21, 2014 at 12:39 pm
(November 21, 2014 at 10:32 am)shakuntala Wrote: This work points out that mathematics ends in meaninglessness for 4 reasons

1) maths proves s 1=0.999.. ie a finite number= a non-finite number thus a contradiction in terms thus maths ends in self contradiction

First of all, 0.999... is not a "non-finite" number. The notation 0.999... represents a geometric series, namely 9/10 + 9/100 + 9/1000 + ... Its sum is calculated by the formula a/(1 - r); in this particular case a = 9/10 and r = 1/10. Substituting these values in the formula, we get (9/10)/(1 - 1/10) = (9/10)/(9/10) = 1.

There is no "contradiction in terms".

Quote:2) 1+1=1

You are probably confusing Arithmetic with Boolean algebra. In Boolean algebra the symbol '+' does not represent addition; rather it is a logical operator. If "+" means OR, we have 1+1=1; if it represents XOR (exclusive OR), we have 1+1=0.

No meaninglessness there.

Quote:3 ZFC ie axiomatic set theory is inconsistent

The consistency of ZFC can't be proven from within ZFC. This follows from Kurt Gödel's incompleteness theorems.

No meaninglessness, but you may want to look up the relevant Wikipedia article (or some other source) for clarity upon the matter.

Quote:4) mathematics cant tell us what a number is without circularity-thus mathematics is meaningless

For any theory, at least some premises or postulates must be taken for granted; in the case of counting with natural numbers the premises are: 1) 1 is a number; 2) every number has a successor; 3) that successor is unique. The only number taken for granted here, is 1.

Mathematics doesn't need to tell us what a number is; that belongs to the domains of metamathematics and philosophy. It is sufficient that mathematicians are in possession of a system to work with numbers.

To sum up, no meaninglessness according to my book.