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Is 1 = 0.9999......

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Originally posted by: jinduy
to celebrate my 1000th post, i'd like to resurrect this post and say that (barney the dinosaur voice) 2 + 2 is 4!
Click to expand...

2 + 2 = 5

(For large values of 2 and small values of 5)

😛
 
Yes. Think of it this way: if those 9's in the x = 0.999... end at any point, then the answer is no. This is because at the point 10x - x = 9.999... - 0.999... becomes, for example, 10x - x = 9.999 - 0.99 (those nines continue for however long, but are always off by one), thus making the expression not exactly equal to 9. However, since according to this question they do continue forever, then those repeating nines all cancel each other out, therefore making the expression true.
 
Originally posted by: esun
Yes. Think of it this way: if those 9's in the x = 0.999... end at any point, then the answer is no. This is because at the point 10x - x = 9.999... - 0.999... becomes, for example, 10x - x = 9.999 - 9.99 (those nines continue for however long, but are always off by one), thus making the expression not exactly equal to 9. However, since according to this question they do continue forever, then those repeating nines all cancel each other out, therefore making the expression true.
Click to expand...

Nonsense. The division never occurs in the first place because there is no practical way to represent the operation without voodoo math.

 
Originally posted by: pkananen
any competant (sp?) math prof. will tell you it does indeed equal 1
Click to expand...

Any competent math prof wouldn't use the questionable notation of .9999....; they would use an infinite sum which would allow them to prove it with a standard epsilon/delta proof.
 
This is not true..... .9999999 does not equal 1

Even in a real life scenario. If you shoot a rocket to the moon, or better yet, pluto. The angle of your rocket is set at 1... you fire the rocket and it hits pluto. Then you reset the rocket at an angle of .999999999 (When in real life you can not set an infinite, however, you would have to stop somewhere.... Your rocket may still hit but it would be a significant difference from the first one fired. No?
 
Originally posted by: ryzmah
Originally posted by: pkananen
any competant (sp?) math prof. will tell you it does indeed equal 1
Click to expand...

Any competent math prof wouldn't use the questionable notation of .9999....; they would use an infinite sum which would allow them to prove it with a standard epsilon/delta proof.
Click to expand...

what difference does the notation make??
 
I was watching Star Wars Episode .99999999999999999... the other day and I got to thinking,
this thread is too long.

 
Originally posted by: Hector13
Originally posted by: ryzmah
Originally posted by: pkananen
any competant (sp?) math prof. will tell you it does indeed equal 1
Click to expand...

Any competent math prof wouldn't use the questionable notation of .9999....; they would use an infinite sum which would allow them to prove it with a standard epsilon/delta proof.
Click to expand...

what difference does the notation make??
Click to expand...

Infinite sums are well defined in mathematics and a proof can be traced back to the base assertions of set theory or potentially category theory. .... is not well defined. If you can't clearly define something in mathematical terms you can't trace a proof back to fundamental axioms - you would have to make an axiom to define ... and your definition makes the answer useless for proof unless it's accepted by those you're trying to convince. Half the challenge in modern algebra and real analysis is making sure everything you use is well defined.
 
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