.99999... = 1 (again)

[Ferrous]

Time for magic math

x = 0.999...
--------------------------------
10x = 9.999.....
--------------------------------
10x - x = 9.999.... - 0.999.....
--------------------------------
9x = 9
--------------------------------
x = 1
--------------------------------
0.99.. = 1

case closed *shuts book*

There is another way to prove this:

1/9= .11111
2/9= .22222
...

8/9= .88889
9/9= .99999

And yes, that is a real proof. Look it up.

 

[DiMono]

Wow, big ups to Mage for using circular logic in an efficient way. "We're trying to prove this, so let's assume it's false, but it can't be false because we're trying to prove it's true, therefore it's true." I don't mean to offend, I just found it amusing.

The proof I was offered in school is

1/9 = .1111111...
multiply both sides by 9 to get
1 = .9999999...

 

[SaroDarksbane]

You guys are still arguing?

From the head of the math department at Oregon Tech:

Yes .9999999. . . is = 1. The best way to show it is with the infinite series you mention. If you have your calculus book, look up geometric series. The first term is .9 and the common ratio is .1 Anytime the common Ratio is between -1 and 1 the series has a finite sum. It is: a/(1 - r) and in our case that is .9/ (1 - .1) = 1.

There are those who argue that the limit only "approaches" 1, but there are many times when it is shown to be equal to 1.
Reasoning with infinity or infinitesimals is always a time to be careful! It is a time when mathematicians use those proofs with epsilon and delta that were talked about briefly when we were learning about limits in 251.

Take from that what you may.

 

[FenrisWulf]

@DiMono:
I'm not sure what's amusing about that; it's simply a standard proof by contradiction. If you assume something to be true, and this assumption leads you to a contradiction, then the opposite must be true.

 

[Sein Schatten]

As much as I hate to revive this topic, I ran into something cool while working on a problem set for my math reasoning class:

"Every nonzero real number has a unique representation as a nonterminating decimal. (If a number has a decimal representation of finite length, reduce the last nonzero digit by 1 and append an infinite string of 9s. For example, 2.38 = 2.3799999. . .)"

No proof was offered, and I get the impression that mathematicians have simply defined real numbers in this way, and as such this may not be explicitly provable since it is definition about real numbers.

So 1=.9999... by definition, no proof necessary. Yay.

thats partly true. the real numbers are rational numbers and irational numbers. your definiton is a definiton for irrational numbers.

 

[SuggestiveName]

thats partly true. the real numbers are rational numbers and irational numbers. your definiton is a definiton for irrational numbers.

No it isn't. Read it again: any real number can be represented as a nonterminating decimal expansion. If it terminates, as in the example 2.38 (clearly rational: 2.38= 119/500) what you do, by definition, is reduce the last nonzero digit by 1 and append repeating 9's. So 2.38= 2.379999... This is ONE definition of the real numbers according to ONE math textbook.

Irrational numbers are defined as numbers are not rational. Rational numbers can be represented as x/y where x and y are both integers. They look like nonrepeatng never ending decimal expansions, but that isn't the definition.

 

[Bob_barker101]

hehehe

i think your all going to die

You need to realize that your childish behaviour is going to get you booted.

Ok, you can't say you haven't been warned.

Freet