0.99999... = 1

[Harrypotter_fan]

Well exactly, that was my point, which I was trying to explain, if we can't perform operations on infinity, because its just a concept, we shouldn't be able to perform operations on things involved in it either.

Ah well, I wouldn't debate any more, looks like no one is catching my drift, and I don't want to get caught in some serious firepower. I'm not arguing the basis of mathematics, its just that... there is something here that is unbelievable. For an approximation, fine, but definitely not for the equality.

Here:

If anyone doesn't believe 0.999.... = 1, then give the P/Q form of 0.999.... As it is a rational number (recurring) and rational numbers can be represented by P/Q.

 

[Kshitiz_Indian]

Here:

That again involves expressions on the infinite concept, because you're subtracting infinite 0.9999... from 9.99999.... something which has no end.

This is all so confusing. I guess soon we'll have someone who'll explain such strange phenomenon with some good logic!

 

[ZoraxDoom]

0.999 isn't = 1 because Equal To means The Exact Same Value No matter how small or insignificant, there is a difference, so it isn't equal to.
It may be widely accepted, easier to use, assumed as, that's all fine. But it is NOT equal too.

 

[zimrahil]

0.999 isn't = 1 because Equal To means The Exact Same Value No matter how small or insignificant, there is a difference, so it isn't equal to.
It may be widely accepted, easier to use, assumed as, that's all fine. But it is NOT equal too.

So tempted to close this thread after this excellent post, but I await the genuis who tries to convince me that a number other than 1 can EQUAL 1

 

[shravi]

[Janice impersonation] OH. MY. GAWD. [/Janice impersonation]

 

[Deleted member 9102]

Edit: Chris Gayle

 

[tassietiger]

0.999 isn't = 1 because Equal To means The Exact Same Value No matter how small or insignificant, there is a difference, so it isn't equal to.
It may be widely accepted, easier to use, assumed as, that's all fine. But it is NOT equal too.

We aren't talking about 0.999. I know that 0.999 doesn't equal one. We're talking about 0.999..., a theoretical number which would go on forever and ever.

The number is made by having 9s after the decimal place until the number actually equals one. Obviously, the number won't equal one when you keep writing 9s there, but it will get closer and closer to doing so as you write them. This is why the number is a recurring decimal.

Infinity is another concept, not a number. When you are getting closer and closer to something, you will actually get there once the sequence goes to infinity. This doesn't happen by writing the number out though, as it's only a concept. 0.999... is the idea of a decimal that repeats the number 9 to infinity decimal places. If it did, then the number which it is getting closer and closer to as more 9s are being written is 1. Therefore, 0.999... = 1

The whole idea of your post was that a number had to be exactly the same, but you're not looking at it right. 0.999... is not heaps of 9s after a decimal place. It is a representation of a sequence which is equal to 1. It is a bit like saying 1/4 can't equal 0.25, just because they don't look exactly the same.

There are a few posts seeming to suggest someone is going to come along and bring some more logic to this, I'm sorry if you don't understand what I'm saying, but it is unlikely to be much simpler than the way I've just explained it.

 

[Deleted member 13648]

Suddenly, tassie doesn't seem so funny any more

 

[Chetan0304]

1 = 1
0.9999.... = 0.9999....

Simple.

Here we have a Genius

chetan0304 added 2 Minutes and 4 Seconds later...

Wow the first post By Shreyas Confused me more..

We know that,
(1 / 3) = 0.33333...
Multiplying both sides by 3,
1 = 0.99999...

But the difference between 1 and (0.99999...) is (0.00000...1).
And that implies that (0.00000...1) = 0.

 

[Harrypotter_fan]

That again involves expressions on the infinite concept, because you're subtracting infinite 0.9999... from 9.99999.... something which has no end.

This is all so confusing. I guess soon we'll have someone who'll explain such strange phenomenon with some good logic!

Then express 0.999... as P/Q. As it is a rational number we should be able to express it as P/Q.

 

[khalek]

Damn you guys are too good in Maths

 

[ZoraxDoom]

I don't believe or like that concept of Infinity then. I understand what you are saying, but I don't understand how people will accept that 0.999...infinity is equal to 1. I don't like it. It's just a conceptual view that if you get closer and closer to something, you will eventually get there, but it is like dividing a number by 2, diving the result by 2, divide that by 2, and so on till infinity. You get closer and closer to 0, and after a while you can take it as 0 for practical use, but it should never, truely, be equal to 0.

If you want to consider 0.999 reocurring equal to 1 for practical reasons, then fine, but it should really never, ever be exactly equal to 1. Maybe it is in the concept of inifity, but not to me.

 

[Harrypotter_fan]

I don't believe or like that concept of Infinity then. I understand what you are saying, but I don't understand how people will accept that 0.999...infinity is equal to 1. I don't like it. It's just a conceptual view that if you get closer and closer to something, you will eventually get there, but it is like dividing a number by 2, diving the result by 2, divide that by 2, and so on till infinity. You get closer and closer to 0, and after a while you can take it as 0 for practical use, but it should never, truely, be equal to 0.

If you want to consider 0.999 reocurring equal to 1 for practical reasons, then fine, but it should really never, ever be exactly equal to 1. Maybe it is in the concept of inifity, but not to me.

Can you answer this?

Then express 0.999... as P/Q. As it is a rational number we should be able to express it as P/Q.

 

[ZoraxDoom]

Nope. 1/3 or 0.333...etc. is an irrational number.

 

[Harrypotter_fan]

Nope. 1/3 or 0.333...etc. is an irrational number.

Are you out of your mind? Any recurring or terminating decimal is rational.