Does .999 repeating equal 1?

[Hauldren Collider]

Asher, computers are finite. Of course you won't have .999 repeating. Your comparison is nonsense.

Also, math has binary truths and literal comparisons. Computer Science is math. It's applied math.

[Asher]

Computer Science is math. It's applied math.

I prefer to think of math as useless computer science.

[loinburger]

In what programming language would the statement:
".999 repeating" == 1
be true?

Mathematica, and possibly Matlab, though that's just reinforcing your point

[Vanguard]

It's not self-contradictory. How does replacing 9 with 8.999... contradict 1 = .999... ? You're not making any sense.

Tedious. But I suppose I asked for it.

Let x = 0.999...

Then 10x = 9.999...

So 10x - x = 9x = 9.999... - 0.999... = 9.

Since 9x = 9, we have that x = 1.


Therefore, 0.999... = 1.

Look at the line in bold. If that '9' is changed to an '8.999...', then what is 9x?

It is:

8.999 / 9

Does this equal 1? At first approximation it does not appear to. It appears to equal

.999...

Which means that Starfish does not prove that 'x = 1', he proves that:

x = .999...,

which we already knew.


Go it?

[giblets]

Tedious. But I suppose I asked for it.



Look at the line in bold. If that '9' is changed to an '8.999...', then what is 9x?

It is:

8.999 / 9

Does this equal 1? At first approximation it does not appear to. It appears to equal

.999...

Which means that Starfish proves that:

.999... = .999..., which we already knew.

Go it?

You can change '9' to '8.999...' if '.999...' equals '1' if you wish but you DON'T HAVE TO DO THAT. Before you made that substitution, you had 9x = 9. That's why the proof works. You didn't provide any argument against it, all you did was make a change to the proof that was based on the assumption that the proof was true. wow, you found that if the proof is true then .999... is equal to .999...

Are you trolling or stupid?

[Vanguard]

Are you trolling or stupid?

Neither. I am responding to someone else's troll post seriously. I find that to be more enjoyable than trolling. I actually view myself as more of a troll facilitator than a troll.

[giblets]

Neither. I am responding to someone else's troll post seriously. I find that to be more enjoyable than trolling. I actually view myself as more of a troll facilitator than a troll.

I'm not trolling. I don't think Skyfish was trolling either. It's hardly trolling to post a valid, well-known proof of a mathematical fact or wonder how someone could manage to think it's "self-contradictory".

[Lorizael]

[Vanguard]

I'm not trolling. I don't think Skyfish was trolling either. It's hardly trolling to post a valid, well-known proof of a mathematical fact or wonder how someone could manage to think it's "self-contradictory".

It is a false proof. They are all false proofs.

Which is not to say that they are false. 999... does equal 1. But only because it is defined to be such, based on our profound mathematical intuition that this is the only way to deal with the situation.

Simply put, the only way to make one number equal to another number is to define them as equal. Otherwise they wouldn't both be numbers.

[Lorizael]

It is a false proof. They are all false proofs.

Which is not to say that they are false. 999... does equal 1. But only because it is defined to be such, based on our profound mathematical intuition that this is the only way to deal with the situation.

Simply put, the only way to make one number equal to another number is to define them as equal. Otherwise they wouldn't both be numbers.

Duh. Similarly, the only reason 1.5 and 3/2 are the same number is because we define them to be. They're not actually the same, because it's not as if humans have the capacity to represent the same idea in two different ways or anything.

[giblets]

It is a false proof. They are all false proofs.

Which is not to say that they are false. 999... does equal 1. But only because it is defined to be such, based on our profound mathematical intuition that this is the only way to deal with the situation.

Simply put, the only way to make one number equal to another number is to define them as equal. Otherwise they wouldn't both be numbers.

This sounds like postmodernist crap.

[Vanguard]

Duh. Similarly, the only reason 1.5 and 3/2 are the same number is because we define them to be. They're not actually the same, because it's not as if humans have the capacity to represent the same idea in two different ways or anything.

Not true. 1.5 is not defined to be equal to 3/2. It can be calculated based on fundamental mathematical definitions. You cannot calculate that .999... is equal to 1.

[Lorizael]

Yes, you can, through the concept of limits of infinite series. Jesus.

[loinburger]

The sum of an infinite geometric series is a/(1-r) where a is the initial term and r is the ratio between successive terms; .9-repeating is the geometric series with .9 as the initial term and .1 as the ratio between successive terms, which results in the sum .9/(1-.1) = .9/.9 = 1

Now enough with this post-modern horse****

[Vanguard]

Yes, you can, through the concept of limits of infinite series. Jesus.

No. The limit of an infinite series can only be used to prove the equivalence of a variable and a number. It cannot be used to prove the equivalence of two numbers. To do so would require us to cancel out a variable that includes, somewhere within it, a hidden infinity. But you cannot do this, because as soon as an infinity enters the denominator of a term, that term becomes undefined.

This is what most proofs of this proposition do. They hide an infinity in one of the variables and then cancel that variable out.