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Simple mathematical problem (?)

Here's my quick take on it...

.999~ is not a measurement. It does not occur in any instance as an identifable value on its own. It only occurs as a result of division. In every case where it does occur as a result of division, the other side of the equation can be either simplified or expanded to be shown as equal to 1.

The only reason the equation would come out to .999~ instead of 1 is because of the conversion from fraction to decimal. Reexamining the fraction in a context compatible to the decimal system will always show .999~ as being equal to 1.

Dividing one item into three parts in the fraction system gives each part a value of 1/3. Reassembling these parts gives an item of value 3/3. Using the decimal system, dividing that same item into three parts gives each part a value of .333~. Reassembling them gives the item a value of .999~.

Both are identical except in the way that they are noted, meaning .999~ certainly does equal 1, and can be shown in all occurances that it will always equal 1.
 
ArmchairPhysicist said:
Here's my quick take on it...

.999~ is not a measurement. It does not occur in any instance as an identifable value on its own. It only occurs as a result of division. In every case where it does occur as a result of division, the other side of the equation can be either simplified or expanded to be shown as equal to 1.

The only reason the equation would come out to .999~ instead of 1 is because of the conversion from fraction to decimal. Reexamining the fraction in a context compatible to the decimal system will always show .999~ as being equal to 1.

Dividing one item into three parts in the fraction system gives each part a value of 1/3. Reassembling these parts gives an item of value 3/3. Using the decimal system, dividing that same item into three parts gives each part a value of .333~. Reassembling them gives the item a value of .999~.

Both are identical except in the way that they are noted, meaning .999~ certainly does equal 1, and can be shown in all occurances that it will always equal 1.
Click to expand...
This is the best explanation yet for the people who don't get it.

Do the long division the way you learned it in elementary school. You can either come up with 1 or .99999... Either way, you will be correct. Yet both answers come from the same problem (e.g., 5 / 5 = ? ), so they are in fact the same.

That .9999...looks different compared with 1 makes it no less the same than 1.0000... looking different copmpared with 1.
 
Snide said:
That .9999...looks different compared with 1 makes it no less the same than 1.0000... looking different copmpared with 1.
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Or that 10<sub>8</sub> = 8 (different ways of writing the same number)
 
xouper said:
Really? It didn't seem to do much good when I mentioned that back on October 29th, on page three:

http://www.randi.org/vbulletin/showthread.php?s=&postid=1870164618#post1870164618
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Sorry, xouper...just 'cause it's the best doesn't guarantee 100% success! :D

I wondered why it hadn't been mentioned earlier. I quit following the thread some time ago, and revisited after you referred to it in the "Best of JREF" thread.

Anyone who still doesn't get it likely never will.
 
Maybe it's in the presentation.
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Of course, it was the same thing, just different words.

Sometimes, even something simple needs to be explained five different ways for five different people to understand it. It might even take five more explainations just to get that sixth person to understand.
 
thread must die die thread stopstop must die thread pointless die please let thread die must stop no no thread die die u thread die stop please die head hurt blood stab blood scream thread die stop no no no stab die..............................................
 
T'ai Chi said:
Any other math things we could argue over?
:D
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Sure, x<sup>0</sup> = 1, where x > 0

I'd guess that those who continued to argue that 0.9~ was a different number to 1 will have trouble with this one also.

"So 7 multiplied by itself zero times equals 1 ? That's impossible! If you multiply 7 x 7 zero times -- that is, if you DON'T multiply 7 by 7 -- you get zero, you haven't done anything!"
 
xouper said:
Sounds like a topic that deserves a thread of its own. :)
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We're only up to page 15, this thread's just getting warmed up. OK fine, if you want you can CTRL+C, CTRL+V it into a new thread.
 
Here's another approach to the recurring decimal dilemma, from Gardiner, page 136, note 1:

What's the first decimal place of

.12345678901234567890...
+ .87654321098765432109... ?
 
Iconoclast said:

Sure, x<sup>0</sup> = 1, where x > 0

I'd guess that those who continued to argue that 0.9~ was a different number to 1 will have trouble with this one also.
Click to expand...


Those ARE two different numbers.

"So 7 multiplied by itself zero times equals 1 ? That's impossible! If you multiply 7 x 7 zero times -- that is, if you DON'T multiply 7 by 7 -- you get zero, you haven't done anything!"
Click to expand...

Actually, as others have noted on the other thread, the logic you propose above is a side-effect of simplyfying exponents to mean multiplying a number that number of times, rather than looking at it from the logarithmic perspective.
 
Iconoclast: ... those who continued to argue that 0.9~ was a different number to 1

Suggestologist: Those ARE two different numbers.
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I'm amazed that you keep arguing for your ignorance on this point, Sugg. You will never get any mathematician to agree with you. Keep it up and you will remove any remaining doubt that you are a crackpot.

Despite repeated requests, not only have you NOT provided any mathematical proof that 0.999.... is a different number than 1, you have not refuted the proofs that they are the same number.
 
Kullervo: Here's another approach to the recurring decimal dilemma, from Gardiner, page 136, note 1:

What's the first decimal place of

.12345678901234567890...
+ .87654321098765432109... ?
Click to expand...
Which is the same as asking what is the sum of the following two fractions

1234567890 / 9999999999
8765432109 / 9999999999
 
xouper said:
I'm amazed that you keep arguing for your ignorance on this point, Sugg. You will never get any mathematician to agree with you. Keep it up and you will remove any remaining doubt that you are a crackpot.

Despite repeated requests, not only have you NOT provided any mathematical proof that 0.999.... is a different number than 1, you have not refuted the proofs that they are the same number.
Click to expand...

It is impossible to "refute" a tautology at the same logical level as the tautology.
 
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