You really think wikipedia is the best source for debate!?!? Do you get all your opinions there?

Not this again... following tvrocks' thread was painful.
It's not a matter of philosophy, it's a matter of mathematical proofs. I'm sure someone will have already posted one or a few before I finish typing, so I'll refrain from posting them.

Well nobody did yet!

I'll start with the fact that:

1/3 = 0.3(repeating)

.9(repeating)/3 = 0.3(repeating)

Therefore, by the transitive property of equality, 1=.9(repeating)

No. :-) But any discussion I would be contributing would be pretty much copy-pasta from anything on that page. It's math, there isn't really anything to debate.

There are several options for proofs contained right on that page, all of which I have nothing to disagree with about.

I think it doesn't. There will always be a difference which causes them to have different properties. The idea of it being that because if limits is also flawed as when you actually go to the limit at 0 in an equation such as (x+5)^2/x at x it would not actually be that timit, it would just be undefined. It also does not work algebraically, conceptually, and all arguments for it are weak.

Ig, you assumed that 1/3 actually equals .3 repeating. If you divided 1 by 3 and .9 repeating by 3 you would see that one of them would yield a remainder.

1 will also yield a rational bumber when divided by 5 while .9 repewting whill not and will foever have a remainder. Using the same ides, 1.9 repeating is odd while 2 is even. Any of these situations you come up with would have these 2 numbers yield very significant properties,

*very significantly different properties. I will try to read through my posts more often from now on. Just as a heads up, i inted to only devkte an hour at most in proving that it doesn't.

Argh, @Ish, you summoned the denialist.

Just no, @tvrocks, no. Go read the wikipedia page. Carefully. It will even acknowledge your point that depending on how you define a number system, you can define one that has the property where 0.9(repeater) is *not* equal to 1 because they are different by a non-zero infinitesimal quantity.

But in the standard real number definition, the difference is actually zero.

In any case, I'm really just going to mute this thread now. This isn't a topic there's any debate about - the whole question is straight up provable mathematics in several ways. If you don't want to believe it, that's fine, but it isn't really a topic there's a question about in mathematics.

Yes. Absolutely.
The sum of all positive numbers also equals -1/12

Remainders don't exist. Remainders, to the best of my knowledge, are not used in algebra, since you can simply go to a decimal.

A=0.9999999......
10A=9.999999.....
10A=9+A
9A=9
A=1

One of the many proofs.

Before trying to say that the argument that .999... +1/i=1is not true because 1/i is not real i think that you should first realize that .999... Is also not a real number. Besides, according to all logic/ mathematics, that equation would be true. (Why else would there be a remainder in 1/3 while there is not in .999.../3? The theory doesn't explain that.)(on another topic, i found this to be extremely interesting. 1/7 = 0.142857142857... and 142 + 857 = 999.)

This is the more important one to talk about.
1+2+3+4+5+6......... to ∞ = -1/12
I kid you not. Look it up.

@ig: defining a number as being equal to something because it is "close" and getting rid of remainders is a very bad idea as, in order to be a number there needs to be no difference, not just an arbitrarily small difference.

@flum: that opens a completely new topic of discussion. If you believe that the laws of mathematics should apply in all situations, then whenever you multiply anything by 10, there will be 1 less significant digit (science term) behind the decimal point. (Ex, 3.3(10)=33 . If you subtract that by 3.3 there will be a difference.) if you don't think it would apply then please give another rule and explain why it would work in that situation, and also test to see if it works in any other situation. If you feel it is unnecessary then you are under the false impression that because the math community in general believes it that i have the burden of proof when you are the one trying to disprove a literally universal law.

The proposed value can effectively be considered equal in a 10 digit system, though in pure mathematics it is a dangerous assumption to qualify them as the same.

Decimals suck

I agree competely. In a dozzenicimal system many of these problems would be solved(although a lot more would come up.) thus is why i prefer fractions.

@tvrocks

I have no idea what language "dozzenicimal" is from, but if you mean a base-12 number system, the word you're looking for is "dodecimal".

Or "duodecimal", more commonly.

@ig: I looked up the number for 12 years and it was dozenial. As a decade is in the same situation I tried converting it. Sorry if it was not correct, I had never heard the term before.

Also, not only is .9(repeating) real, but it is rational. If you think that a number with infinite digits is not real, that would rule out the sqrt. of 2 as well, along with pi and any other irrational numbers (which are part of the real number set).

sqr rt of 2 is impossible to write on a 10 digit decimal system, or even in a fraction. I will admit, that assertion was not very well thought through. (I guess it could be written as .333... (3). Please explain why 1/infinty, the definition of infinitesimal, would not be real.

An infinitesimal value is the inverse of infinity, which is not real. Therefore, infinitesimal is not real.

An infinitesimal value does not react to any real number (except possibly zero). Multiply it by two, and what do you get? 2/infinity? Regardless, it is the same value. The only real number that has this form of identity property of multiplication, is zero.

Assuming 1/inf is a real number, for a moment, it would *have* to be equal to zero. Which means it IS zero. Which means (1-.9repeating) = 1/inf = 0. Which means .9repeating equals 1.

You can disprove the idea that 1/info is 0 using simple arithmetic. :) If you multiplied 1/inf by 2 then it should be 2 times that original 1/inf . This idea is reliant on the 2 infinities being equal to each other which, should be true, but I donMt feel like explaining it in this thread. If you want an explanation to to the thread I made a few months ago. Try representkmg infinity with x and it will be clear that it would be true. You could also multiply by "x" in order to get the correct answer.

@tvrocks
how does that disprove that idea at all? 2x 0 is also 2 times the original number, 0. What's your point?

I was leaving it to you to disprove the idea using arithmetic. If you set up the equation 1/inf=0 and multiply by inf on both sides it will end up being 1=0 which is not true. It also works conceptually. (no matter how big the thing in the numerator is, it is impossible to get rid of the number in the numerator.)

inf(0) =/= 0

inf/inf =/= 1

you realize that 0xinf is indeterminte right? so is inf/inf. You can't use algebra on infinity