0.9_ = 1?

Post Reply New Topic

But arbitrarily close is. Perhaps you should learn what a limit in mathematics is.

ruveyn

that is very liberal of you.

ruvyen

I know what a limit is, kid. I am an Electrical Engineer! I work with the Calculus every day. I also know what an "asymptote" is, and when to say "Meh ... close enough ... let's stop adding decimal points and just put it into production!"

While "close" may be "good enough" for practical purposes, it is never "exact." You may as well argue whether 9999999 or 9999999999999999 angels can dance on the head of a pin, as it makes just as much difference in the real world. Really. So while your argument may have some value as a time-waster, it has no value in a practical application.

just because a limit approaches something does not mean that it ever equals that. You can't arbitrarily drop out the limit and say "hey look what this equals"


arbitrarily close just means arbitrarily close.

do you call division by 0 undefined or infinity?

math to engineer odd-ball question.

In a division ring, it is undefined. In the theory of hyper-reals it gets a little more complicated.

ruveyn

I have seen this happen a dozen times on sci.math on usenet. It is amazing. There is a hard core of people who simply do not understand limits and convergence.

ruveyn

you can say lim .999999999(etc.) approaches 1. You cannot say .999999999(etc.) equals 1. Because you cannot just drop the limit off.

if you did that you could just say 1/x is zero. but it is not. unless you take the lim as x goes to infinity. but you can't just drop off parts of equations as say it is all and well.

I am saying that lim .999999999(etc.) = 1 but .999999999(etc.) does not equal 1. You can say .999999999(etc.) approaches 1, but you cannot say it equals 1. it is the limit that equals 1 and not the number.

One built-in assumption that a lot of people have which makes 0.9_=1 "counterintuitive" is that every real number is uniquely expressed in decimal notation. That's not the case. You can, if you like, consider a proof of 0.9_=1 to also be a proof that you can't express real numbers uniquely in such a fashion.

However, you might just not want to work with a continuum. But then you're essentially talking about something else.

Why are you saying that c=1? c can equal any number, (in this case, 0.9_) and you can't divide c by c without dividing 0.9_ by c, which is impossible. It might also be worth mentioning that 1 is an integer and 0.9_ isn't.

Thank you for proving my assertion. The expression .9999(etc) is a limit. It is the limit of the sequence {.9, .99, .999 ....} where the n-th term is .999 (n times). The limit of a sequence or real numbers is a particular real number if the limit exists. Limits don't approach anything. Terms of sequences sometimes do.

ruveyn

They say 9.999...-0.999...=8.999..., which is subtracting 1. Also, 0.999... IS an integer, since it is equal to 1. When at first I didn't believe this, I thought, "You can say all numbers are equal, since 0.999...=0.999...98=0.999...97, etc." However, there is no such thing as 0.999...8, since there are infinitely many 9s, so you will never actually get to the 8.

Uncyclopedia is, as far as I can tell, a comedy site. Nearly everything said about mathematics there is invalid in a supposedly humorous fashion.

In particular, let's look at the algebraic proof.

This is an invalid assumption to make about repeating decimals. In any case, I'm not sure how it pertains to the next section, because if you do make this assumption then you can't do what they do next.

What they do here is quite subtle and probably only funny to someone who has seen the "algebraic proof" before. The "algebraic proof" as I'm familiar with it (which, by the way, I do not endorse as a rigorous proof) goes like this:
1. Take x=0.9_
2. Multiplying x by ten gives 10x=9.9_ (note: there is an implicit assumption here that if you multiply a number with a recurring decimal by ten you still have a recurring decimal, which is correct, but is the reason why I don't accept this as a rigorous proof for someone not convinced that 0.9_=1. After all, some may falsely assert like in the Uncyclopedia article that 10x "has one less nine at the end" than x)
3. 10x-x=9x=9.9_-0.9_=9
4. x=9/9=1

I laughed out loud when the Uncyclopedia writer said "but the answer is 8.9_". In order to do this, you have to assume that 9.9_-0.9_=9.9_-1, or in other words 0.9_=1. I'm guessing this was the point of the Uncyclopedia writer's joke, but as I've said it's quite subtle. Of course, if you then accept that 0.9_=1 then you can also accept that 8.9_/9=9/9=1.

The "fraction proof" and "proof by induction" are the kinds of jokes I could imagine one of my classmates telling me in high school. The existence of "0.0_1" is not validly deduced. The "geometric proof" makes a calculation error and then uses it to conjure up a fallacious argument to produce the desired conclusion.

It's encouraging that you're taking an active interest in mathematics, in particular mathematics which I didn't really understand until a few years ago, but don't be persuaded by faulty reasoning disguised as humour. Think critically!

An integer is any number that only has 0's after its decimal point. 0.9_ obviously isn't an integer and if 1 is equal to 0.9_ then 1 wouldn't be a integer either, but 1 is an integer and 0.9_ therefore isn’t equal to 1.

An integer is any number that only has 0's after its decimal point. 0.9_ obviously isn't an integer and if 1 is equal to 0.9_ then 1 wouldn't be a integer either, but 1 is an integer and 0.9_ therefore isn’t equal to 1.[/quote]

Learn to troll better.

Also, the only truthful article on Uncyclopedia is the Scientology page, because they couldn't come up with anything more bat s**t crazy then that.

I just think it is clear that 0.9_ is a number between 0 and 1 and that it keeps getting closer to 1 but never gets there. I don’t mean to troll. (to be honest, I hardly even know what troll means, I fail at internet slang, lol)