Message Board Basketball Forum - InsideHoops OT: "Interesting" Math Question 2
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09-09-2006, 02:37 PM   #211
IceMan2
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And like I said...

The equation
Quote:
 x=0.9r 10x=9.9r 10x-x=9.9r-.9r 9x=9 x=1 x=1=0.9r

It is true

This is just a basic equaiton of equality

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

 09-09-2006, 02:52 PM #212 raiderfan19 Shazam!     Join Date: Jun 2006 Posts: 7,012 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.
09-09-2006, 03:49 PM   #213
IceMan2
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Join Date: Aug 2006
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Quote:
 Originally Posted by raiderfan19 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

 09-09-2006, 03:51 PM #214 raiderfan19 Shazam!     Join Date: Jun 2006 Posts: 7,012 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.
09-09-2006, 03:59 PM   #215
IceMan2
Local High School Star

Join Date: Aug 2006
Posts: 1,828

Quote:
 Originally Posted by raiderfan19 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...

So how is the value changed?

"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

 09-09-2006, 04:08 PM #216 cookiemonster I hit open layups   Join Date: Jun 2006 Posts: 154 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.
09-09-2006, 04:13 PM   #217
IceMan2
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Join Date: Aug 2006
Posts: 1,828

Quote:
 Originally Posted by cookiemonster 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.
Thank You

 09-09-2006, 04:16 PM #218 raiderfan19 Shazam!     Join Date: Jun 2006 Posts: 7,012 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.
09-09-2006, 04:27 PM   #219
I hit open layups

Join Date: Jun 2006
Posts: 154

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.

09-09-2006, 04:34 PM   #220
IceMan2
Local High School Star

Join Date: Aug 2006
Posts: 1,828

Quote:
 Originally Posted by cookiemonster 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
Trust me...I have tried that

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