Thread: Does 0.9 repeated = 1?

You can also see the proof in certain graphs. 1/x-1 for example cannot equal 1, but its value rises or drops indefinitely as it approaches the asymptote. And no matter how close the value gets to 1 (in other words, how many times 9 is repeated), it is never equal to one.

Asking if .9999999~ repeated is equal to a rational number is like asking the same of infinity. The answer is that it's not a number to begin with, but an irrational system: a term we use to stand for something our minds couldn't normally contend with. Sort of like how we use i to stand for the square root of a -1 (which can't exist, but it's still an essential component of mathematics).

Originally Posted by Tamias.Squirrel

Asking if .9999999~ repeated is equal to a rational number is like asking the same of infinity.

NO.

The answer is that it's not a number to begin with, but an irrational system:

ABSOLUTELY NOT.

1/3 is clearly a real, rational number. Look at its decimal representation:

.333....

IT IS A NUMBER. Irrational system? It is one single number. It doesn't do anything. It is as solid as 2 or 3 or 1/5 or 3/7.

You can't take a third of a pie and then say that pie's calculating itself out to infinity. You just have a third of a pie. And if you have three thirds, you have one whole, equal to .999... of the pie.

Remind me never to have a debate with you.

Fine by me.

Originally Posted by hungrymanz

NO.

You can't take a third of a pie and then say that pie's calculating itself out to infinity. You just have a third of a pie. And if you have three thirds, you have one whole, equal to .999... of the pie.

That's actually a good point xD Hmm... This is a lot more complicated than I first thought. Maybe we should all just agree that nobody really knows?

Lol, sure.

Originally Posted by xXSomeGuyXx

O_O See ya in a few weeks...lol. Those actually look fun.

Hint: There's no exact answer for either of them. Kinda blows your mind if you think about that fact.

EDIT: One thing. The first equation has a trivial solution x=0. I want the non-trivial solution.

Originally Posted by Tamias.Squirrel

That's actually a good point xD Hmm... This is a lot more complicated than I first thought. Maybe we should all just agree that nobody really knows?

No, we do know. It has been proven dozens of different ways, including real number construction, the be-all end-all proof of numbers, that 0.9~ DOES EQUAL 1.

Well, yeah., Ima go use a table of solutions.

Question, exp(x) is to the xth power, correct?

Originally Posted by xXSomeGuyXx

Question, exp(x) is to the xth power, correct?

exp(x) is e^x, where e is the usual e

What about this?

There are no numbers between 1.000...1 and 1, right?

So they are the same, because adding the one to the end is redundant.

So basically, .999... is just 1 - 0.000...1, which is zero, making .999... 1.

Originally Posted by drewmandan

No, we do know. It has been proven dozens of different ways, including real number construction, the be-all end-all proof of numbers, that 0.9~ DOES EQUAL 1.

He is right. Maybe you don't understand it, Tamias, but there are people who do. I encourage you to keep trying to understand it.

Originally Posted by drewmandan

No, we do know. It has been proven dozens of different ways, including real number construction, the be-all end-all proof of numbers, that 0.9~ DOES EQUAL 1.

But it doesn't: Like I said before, the graph 1/x-1 gets infinitely close to 1, but never, ever touches it. The y-values just keep going up or down. So no matter how close to one you 1, you are never exactly on 1.



I guess I don't get it.

Originally Posted by Tamias.Squirrel

But it doesn't: Like I said before, the graph 1/x-1 gets infinitely close to 1, but never, ever touches it.

You have to understand that .999... is a number, not a function or a graph.

I understand that, hungrymanz.
What I don't understand is why this thread continues and people still view the issue as debatable despite being shown the 'proof' that they are the same. It is... fact. It's really that simple. Whether or not it makes sense is irrelevant.

Your logic on the issue is irrevelant.

Human logic means nothing next to numbers!

You are all powerless next to the awsome might of calculus! Understand?