1 = 0,99........

[Danny Boy]

knew it already.

[Ghieri]

Aww... this debate ended before I got here.

Actually, it ended in the first couple of replies. Damn.

[BAndrew]

It's totally irrelevant though. No computer is capable of computing infinitesimals so 1 - 0.9~ on any calculator will always be 1 x 10^-∞. Personally it makes my brain hurt so I have a hard time accepting it.

A calculator is a computer. I realize it is legit on paper but it is simply not practical. Almost all big calculations are handled by computers. You probably already know this, but there is no such thing as infinite memory. The number infinity has no calculable value and the value of 0.9~ requires an infinitesimal to precisely calculate and by definition computers need measurable data to calculate. Therefore neither of these operations are possible to truly calculate on computers. You always need to approximate, and with approximation comes a loss of data.

EDIT: I'm not saying I don't believe it, I just question its usefulness and whether or not the two numbers should be equal. When quantum computers become a reality we will most likely be able to precisely calculate the distance between 0.9~ and 1, because there is one, no matter how small, and the numbers will cease to be equal.

A computer is not the same as a calculator.

A computer can't calculate infinite numbers, but it can calculate the result of infinite series with limits. It doesn't calculate every number as it goes into infinity, as you don't when you are solving something with limits. You don't count into infinity. You use some properties. That's what the computer can do.

This should change your mind:

http://www.wolframalpha.com/input/?i=lim...lk=4&num=1

How did it calculate it if a computer can't?

There is no distance between 0,9~ and 1. If there is it is infinitely small which doesn't make sense. The numbers are the same.

[rndmnwierd]

[Robby]

Lol, rndmnwierd, I had the same thing.

[BAndrew]

Evaluate the following limit:

[Unearthlybrutal]

Simply version

1 / 3 = 0.33333... (infinite 3)
Then:
0.33333... x 3 = 0.9999999... (infinite 9)

(1 = 0.99999999...)

[BAndrew]

Simply version

1 / 3 = 0.33333... (infinite 3)
Then:
0.33333... x 3 = 0.9999999... (infinite 9)

(1 = 0.99999999...)

Although this is not a valid mathematical proof it is very practical! Well done

[Bridge]

A computer is not the same as a calculator.

A computer can't calculate infinite numbers, but it can calculate the result of infinite series with limits. It doesn't calculate every number as it goes into infinity, as you don't when you are solving something with limits. You don't count into infinity. You use some properties. That's what the computer can do.

This should change your mind:

http://www.wolframalpha.com/input/?i=lim...lk=4&num=1

How did it calculate it if a computer can't?

There is no distance between 0,9~ and 1. If there is it is infinitely small which doesn't make sense. The numbers are the same.

1) Look dude, calculators are not magical devices that were just discovered. A calculator is just a small computer that performs only mathematical operations. It has a microprocessor just like a computer, some memory where it can store numbers, a simple means of drawing graphics and a keyboard through which you can input data. That's a fact (look it up!). There is absolutely no difference between computers and calculators other than the fact that dedicated calculators specialize only in mathematics.

2) Well of course! That's basically what I just said. The number infinity is uncountable and therefore cannot be used by a computer at all. Did you even read my post? Memory is finite, and numbers take up a determinable amount of space in memory. If you were truly using infinity, it would take up an infinite amount of bytes, which would mean your memory chips would be larger than the universe. You always need to approximate (you don't think programmers actually type in all of the 500.000 some decimal places Pi has when defining it, do you?).

3) Infinitely small, not non-existent. Computers cannot at the moment calculate infinitesimals but there is a distinct possibility that quantum computers will be able to (since they are millions of times more powerful than the most powerful supercomputer in existence). I don't have any proof, but some day it may be revealed that there does exist a number between 0.9~ and 1. You do realize that at some point people did not believe there were any numbers between 0 and 1. The laws of science and mathematics are volatile.

Now please read my post carefully before responding.

[BAndrew]

A computer is not the same as a calculator.

A computer can't calculate infinite numbers, but it can calculate the result of infinite series with limits. It doesn't calculate every number as it goes into infinity, as you don't when you are solving something with limits. You don't count into infinity. You use some properties. That's what the computer can do.

This should change your mind:

http://www.wolframalpha.com/input/?i=lim...lk=4&num=1

How did it calculate it if a computer can't?

There is no distance between 0,9~ and 1. If there is it is infinitely small which doesn't make sense. The numbers are the same.

1) Look dude, calculators are not magical devices that were just discovered. A calculator is just a small computer that performs only mathematical operations. It has a microprocessor just like a computer, some memory where it can store numbers, a simple means of drawing graphics and a keyboard through which you can input data. That's a fact (look it up!). There is absolutely no difference between computers and calculators other than the fact that dedicated calculators specialize only in mathematics.

2) Well of course! That's basically what I just said. The number infinity is uncountable and therefore cannot be used by a computer at all. Did you even read my post? Memory is finite, and numbers take up a determinable amount of space in memory. If you were truly using infinity, it would take up an infinite amount of bytes, which would mean your memory chips would be larger than the universe. You always need to approximate (you don't think programmers actually type in all of the 500.000 some decimal places Pi has when defining it, do you?).

3) Infinitely small, not non-existent. Computers cannot at the moment calculate infinitesimals but there is a distinct possibility that quantum computers will be able to (since they are millions of times more powerful than the most powerful supercomputer in existence). I don't have any proof, but some day it may be revealed that there does exist a number between 0.9~ and 1. You do realize that at some point people did not believe there were any numbers between 0 and 1. The laws of science and mathematics are volatile.

Now please read my post carefully before responding.

1)My point was that a computer is a more powerful calculator as it does much more things than a calculator, so I will leave this here.

2)I read your post. I agree that a computer cannot calculate infinite digits (like Pi as you said),but what I am trying to tell you is that it doesn't actually calculate them. It uses (let's say) mathematical tricks in order to get the result. It can't calculate Pi itself.

3)We just proved that it is the same number. It's like saying what's the distance from 2 to 2. Unless your are talking about complex numbers and not real numbers that statement doesn't make sense to me.