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Simple mathematical problem (?)

Originally posted by Suggestologist
It is impossible to "refute" a tautology at the same logical level as the tautology.
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Huh?

Isn't a tautology something that's true by definition? So, of course, you can't refute a tautology. Why would you want to? It's true.
 
69dodge said:
Huh?

Isn't a tautology something that's true by definition? So, of course, you can't refute a tautology. Why would you want to? It's true.
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Tautologies are a type of circular reasoning. To refute them, you cannot accept their premises, thus you cannot refute them on the same logical level as they arise.

Xouper is asking me something like:"Prove that orange chickens aren't orange." Well, I can't prove that orange chickens aren't orange. (which relies on an intensional definition) I can only show that chickens are not naturally orange. (which relies on extensional definition)
 
I weep for the mathematical components of our public education system.

Every single time *BASIC MATHEMATICAL PRINCIPLES* are disussed on this forum, someone - and its always someone who is clearly somewhat educated - displays massive mathematical ignorance.
 
Suggestologist: Xouper is asking me something like:"Prove that orange chickens aren't orange." Well, I can't prove that orange chickens aren't orange. (which relies on an intensional definition) I can only show that chickens are not naturally orange. (which relies on extensional definition)
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If you cannot prove that orange chickens are not orange, then stop wasting people's time with your bogus claim that orange chickens are not orange. It doesn't matter if they are "naturally" orange or not.
 
xouper said:
If you cannot prove that orange chickens are not orange, then stop wasting people's time with your bogus claim that orange chickens are not orange. It doesn't matter if they are "naturally" orange or not.
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LOL.

Provide your definition of the decimal number line.
 
Suggestologist said:


Provide your definition of the decimal number line.
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Now that you are back on this thread, could you please answer my question on whether the set of natural numbers N = {0, 1, 2, 3, ... } is finite or infinite?
 
LW said:


Now that you are back on this thread, could you please answer my question on whether the set of natural numbers N = {0, 1, 2, 3, ... } is finite or infinite?
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It's transfinite. Infinite with certain properties that distinguish it from other infinites, such as the number of real numbers.
 
Suggestologist sez: Those ARE two different numbers.

No, they're not. 0.9~ = 1. 1 = 0.9~. End of story. Just stop. Or give us a number that is greater than 0.9~ and less than 1. Or refute any proof in the last 15 pages. Or publish your results and be famous, maybe even win the JREF million.
 
Suggestologist: I see a definition of real numbers. But not of a decimal number line, there.
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I assumed you were using the phrase "decimal number line" to mean the "real numbers". Now that you have clarified that's not what you meant, then I have to ask, what does the "decimal number line" have to do with the equality 0.999... = 1?
 
xouper said:
I assumed you were using the phrase "decimal number line" to mean the "real numbers". Now that you have clarified that's not what you meant, then I have to ask, what does the "decimal number line" have to do with the equality 0.999... = 1?
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.9999.... is a decimal number representation.
 
Originally posted by Suggestologist
.9999.... is a decimal number representation.
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Indeed it is. And the real number that it is a representation of, is, by definition of decimal notation, the same real number that is the limit of the sequence .9, .99, .999, .9999, . . .

What real number is that?
 
69dodge said:
Indeed it is. And the real number that it is a representation of, is, by definition of decimal notation
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Please provide that definition.

, the same real number that is the limit of the sequence .9, .99, .999, .9999, . . .

What real number is that?
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Suggestologist said:
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.
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Well, I don't do smilies, so you're going to have to work out for yourself when I'm acting tongue in cheek, I'd have thought the quotation marks would have clued you in.
 
Originally posted by Suggestologist
Please provide that definition.
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I'm not sure I understand what you're asking for. I did provide the definition. The definition of ".9999. . ." is<blockquote>the limit of the sequence .9, .99, .999, .9999, . . . .</blockquote>Or, if you prefer the general case, the definition of ".d<sub>1</sub>d<sub>2</sub>d<sub>3</sub>d<sub>4</sub>. . .", where the ds are decimal digits, is<blockquote>the limit of the sequence .d<sub>1</sub>, .d<sub>1</sub>d<sub>2</sub>, .d<sub>1</sub>d<sub>2</sub>d<sub>3</sub>, .d<sub>1</sub>d<sub>2</sub>d<sub>3</sub>d<sub>4</sub>, . . . .</blockquote>It really is as simple as that.
 
T'ai Chi

If .9~ = 1,
(.9~ + 1)/2 = 2/2 = 1

If .9~ != 1 then complete the equation....
(.9~ + 1)/2 = ?

BillyJoe
(Yeah, I saw the smilie ;) )
 
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