I’ve suspended you for repeated blogwhoring. Write me if you’d like to explain.

]]>Proof:

1 = 1/3 + 1/3 + 1/3

1/3 = .333…

Therefore,

1 = .333… + .333… + .333…

1 = .999…

Q.E.D.

]]>does 2 – 0.999… == 1?

And the answer is yes.

]]>It’s all in how you define division. One definition of a/b is “what number, multiplied by b, gives a?”. Here, we have 1/2; in other words: “what number, multiplied by 2, gives 1?” When working with integers modulo 7, the answer is 4 (as above).

When working with ordinary integers, there is no such number (the answer doesn’t exist). With integers modulo 8, there is also no such number.

When working with fractions or reals, the number is a half.

The practical importance of this is mostly in cryptography; several well-known ciphers (including RSA) rely on related facts about modular arithmetic.

]]>for a more specific, albeit not as funny, explanation of 2. ]]>

Noen, I just wrote: In before arguments about “0.9999.. = 1″

MeFail

]]>Also, 6.999… is not a “different number than 7″, it is 7.

]]>Auto-Fail

]]>Ah ha ha hahah hah ha…

Are you new to this, or have you just suppressed the horror?

]]>Unfortunately, 1.000…0001 is a nonsensical notation. The “…” ellipsis doesn’t stand for some really large number, like what you’re suggesting. It’s infinite. So it doesn’t make sense to have an infinity of 0’s, and then something after that. It’s not the name of any number, and so it’s not a number at all.

]]>A lot of confusion can be avoided by carefully distinguishing the expressions we use to refer to the numbers (the numerals, along with decimals and slashes), and the numbers themselves (whatever kind of abstract object those are).

]]>So same value, different representation.

Sort of how 0.0, -0 and 0 all have the same value, but are different symbolic representations.

Since one definition of ‘number’ is ‘symbolic representation’, then yes – different numbers.

The whole thing hinges on whether you believe that a symbol and the value it represents are two different things or not.

Ceci n’est pas une pipe.

]]>SEMANTICS!

]]>it’s a math clock, not an atomic clock. One significant digit please.

]]>Assertion: h0.FFF~ = 1 (By similar rule that d0.999~ = 1)

hF > d9 (Hope you agree)

but

h0.FFF~ = d0.999~ (Wait, I thought F > 9…)

Worse yet…

hE < hF (Hope you agree) h0.EEE~ < h0.FFF~ (Hope you agree) hE > d9 (You see where I’m going here…)

h0.EEE~ < d0.999~ (???)
====
Zeno's Paradox approach: You need to get to one. I give you 9/10. Now you need an additional 1/10. I give you 1/100. And so forth. Doing this an infinite number of times is *not going to help. *

And, no, I’m not talking about the number moving or approaching anything, I’m talking about how to determine where that point is by evaluating its representation. I get the feeling that some refutations confuse these two points.

The problem is that saying “an infinite number of nines” is equivalent of saying “and then a miracle occurs”. Yes, there is a place on the number line that represents 1/3, you just can’t accurately express where that place is with base ten digits, *no matter how long you try*. Claiming that it works out if you go to infinity doesn’t help.

In short, a repeating decimal is not a number any more that 1/0. It may be used as a shorthand for a concept, but you can’t do real math with it because it’s inherently inaccurate. Or, if you insist, show your work.

]]>http://en.wikipedia.org/wiki/0.999…

http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/

http://www.straightdope.com/columns/read/2459/an-infinite-question-why-doesnt-999-1

]]>Sweet. ]]>

FWIW, 6.9… is not the same number as 7, but it does have the same value. To say 6.9… = 7 is correct, but 6.9… == 7 is not.

]]>