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

[shakuntala]

This work points out that mathematics ends in meaninglessness for 4 reasons
[SNIP]
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
2) 1+1=1
3 ZFC ie axiomatic set theory is inconsistent
4) mathematics cant tell us what a number is without circularity-thus mathematics is meaningless

[Alex K]

Number 1) is not a proof, nor a problem. It's merely two equivalent ways to write down the same real number. Duh.

I cannot read the linked text.

[Exian]

Number 2) is arrived at by dividing by zero. When is dividing by zero allowed, I ask you?

Also, does this make 1=1 false? Or unusable?

[Chas]

This work points out that mathematics ends in meaninglessness for 4 reasons
[SNIP]
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
2) 1+1=1
3 ZFC ie axiomatic set theory is inconsistent
4) mathematics cant tell us what a number is without circularity-thus mathematics is meaningless

Your ignorance is showing, Google "infinite series".

[Alex K]

Number 2) is arrived at by dividing by zero. When is dividing by zero allowed, I ask you?

There's a whole thread for that

[Smaug]

On the first point. I don't know the historical background that well and can't tell for how long it has been that way (so feel free to correct me) but 0,999... is 1 by definition. The trick is that 0,999... is not just 0,999...9 with a finite number of 9s in between, it's has an infinite number of 9s. Prooving that 0,9... equals exactly 1 had been a sort of a philosophical problem indeed but only before the establishment of Calculus (limits, infinite series and sums in particular). One of the most important concepts of Calculus is a limit. Not going into details, the concept of Limit is a way to understand, to formalize and to deal with certain types of infinity such as the one present above. 0,9... may be represented by an (infinite) power series: 9*10^(-1) + 9*10^(-2) + ...+ 9*10^(-n) + ... . As you can see, it's an infinite sum. Although you obviously can't find the sum by adding all the members one by one Calculus provides a way to calculate it. Now I'm not going to explain all the theorems that allow the following actions, just going to show schematically how that's done. A partial sum is a sum of the first n elements of the series. If you try to calculate several partial sums in this exact case you notice that with an increase of n they get closer and closer to 1. If you make n approach infinity you get a limit of partial sums which is the sum of given infinite series. Formally it looks like this:

lim (sum (9*10^(-n))) = lim (1 - 10^(-n)) = 1 (where n -> infinity)

Let me explain a bit here. The sum in the limit is not an infinite one. It's a partial sum of first n elements of the series so there IS a final n'th term in it. With that in mind, we can rewrite the sum as 1 minus that one 0.00...1 (10^(-n)) that separates the sum from being exactly 1. And after that we proceed to calculate the limit: with an increase of n the term 10^(-n) gets infinitesimaly small and ends up zero when n -> infinity.

To sum it up, 1 = 0,999... was a sort of contradiction untill people got better understanding of the concept of infinity. And no surprise that it's still confusing for those who look at it from an arythmetical point of view.

As for point two, I don't really get what you exactly mean but there are plenty of things that may look paradoxal for people who are not that much into Mathematics. In Abstract Algebra you can come up with sets with some pretty exotic properties. Examples can be also found in Functional Calculus and other highly abstract fields of Mathematics.

As for the rest, I'm not prepared to talk right now.

[BrianSoddingBoru4]

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

What a pointless whinge - ALL definitions are circular. I'm happy you're banned.

Boru

[vorlon13]

Could the mod team ban this miscreant bleen times ???

[Thumpalumpacus]

[agnesi]

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".

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.

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.

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.