But ANY number for x and in the end, it will come out what x equals...if you stick 8 in, you will end up with 8...If you stick 0.4 repeating...Guess what, you'll end up with 0.4 repeating...If you stick 100.5 in , you'll end up with 100.5...........And if you stick 0.9r you'll end up with 1

Its not true. No matter how many 9s you make the first X equal to, when you multiply it by 10, there would be a 0 in the last spot when you subtract the second .9repeating. so essentially it would be

x=.9repeating to infinity

10x=9.9repeating to infinity-1 with a 0 at the end
9x=8.9repeating to infinity - 1 with a 1 at the end
x=.9repeating to infinity.

Its not true. No matter how many 9s you make the first X equal to, when you multiply it by 10, there would be a 0 in the last spot when you subtract the second .9repeating. so essentially it would be

x=.9repeating to infinity

10x=9.9repeating to infinity-1 with a 0 at the end
9x=8.9repeating to infinity - 1 with a 1 at the end
x=.9repeating to infinity.

You do not understand infinity

There is no end to it

Saying things like there would be a 0 in the last spot shows that...

It doesn't have an end...It goes on forever...I don't think you quite understand that...Saying there are numbers after an infinity of 9 is just wrong

Thats my point, when you multiply it by 10 you are changing the value of it. Thats why you cant multiply an infinite decimal in truth. Because it never ends and when you try to use it later in a question you have changed a value.

Thats my point, when you multiply it by 10 you are changing the value of it. Thats why you cant multiply an infinite decimal in truth. Because it never ends and when you try to use it later in a question you have changed a value.

No you aren't

.9r * 10 is 9.9r

There is no changed value

Because the answer is still an infinity...

THink of it this way, for you, I am not thinking of this way

.9r is closest to 1
that must mean
9.9r is closest to 10...

in your theory

So how is the value changed?

Google in

"0.9 repeating equals = 1"

and see what you get...

Regular people just don't get it, becuase they use commen sense, but all the mathmaticians...They no its equal...Thats the difference

oh gosh, listen to me, i'm a mathematician. it IS equal to 1. stop with the nonsense and take any basic mathematical analysis class and have your professor explain it to you.

oh gosh, listen to me, i'm a mathematician. it IS equal to 1. stop with the nonsense and take any basic mathematical analysis class and have your professor explain it to you.

Look dude, i understand ive already explained that for the purposes of equations yes you can subsitute the two because you have essentially no degree of error BUT in theoretical truth, they arent completely equivalent and I have had calc 2 and analysis classes.

You're wrong. They are EXACTLY equal BY DEFINITION. 9.99999999... is just another way of writing 1.

It is simple to prove this by contradiction.

Suppose it is not exactly equal to 1, that they're two separate numbers.

Let a=.9999..... b=1
Since the space of real numbers is compact is a compact set, there exists by neccessity a number c between 9.9999... and 1. a<c<b (strict inequality)

Yet, for any number c that you chose, c<a

Therefore, we have a contradiction... this implies that a=b.

Quote:

Originally Posted by raiderfan19

Look dude, i understand ive already explained that for the purposes of equations yes you can subsitute the two because you have essentially no degree of error BUT in theoretical truth, they arent completely equivalent and I have had calc 2 and analysis classes.

You're wrong. They are EXACTLY equal BY DEFINITION. 9.99999999... is just another way of writing 1.

It is simple to prove this by contradiction.

Suppose it is not exactly equal to 1, that they're two separate numbers.

Let a=.9999..... b=1
Since the space of real numbers is compact is a compact set, there exists by neccessity a number c between 9.9999... and 1. a<c<b (strict inequality)

Yet, for any number c that you chose, c<a

Therefore, we have a contradiction... this implies that a=b.