0.00... means 0 WITH INFINITELY MANY ZEROS AFTER IT, SO ITS EQUAL TO 0
YOU DUMB FUCKS ARE DRIVING ME CRAZY. IF YOU STILL DONT GET IT JUST GO LEARN MATH FOR A COUPLE OF YEARS AND COME BACK
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Anonymous2007-02-21 23:27 ID:f1AaW16/
>>44
Wrong. 0.000... means 0 + 0.0 + 0.00 + ... + 0.0001 which is not equal to 0, dumb fuck. lern2math plz
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Anonymous2007-02-22 1:22 ID:kjwB4oM4
>>40
0*10^n will always be zero, so you can add as many zeroes as you want to a number without changing its value (and therefore without changing it).
As for 0.000...1, that is a malformed number and has no meaning. Consider .123...4, where the ellipsis still represents an infinite number of digits. Each digit is multiplied by 10 to some n proportional to its distance and direction from the decimal point, so .123... can be represented as (1*10^-1)+(2*10^-2)+(3*10^-3)+.... What is n for the 1 in .000...1? The correct application of that hotel thing from earlier tells us that it can't be infinity.
Alternatively, I challenge you to write this number - write an infinitely long string of zeroes, and then put a 1 at the end of it. If you manage to do so, well, that wasn't a very infinite string, was it?
>>43
Troll. That crap where the teacher supposedly tried to create a number for the reciprocal of zero does nothing to resolve the conflict, since 0*(1/0) would equal 0*(nullity), which would still be required to equal both 0 and 1 by 0x=0 and n/n=1.
>>48
0x=0 for all x ∈ ℝ (ℂ, too, unless there's an exception I am missing.)
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Anonymous2007-02-22 18:03 ID:f+L8Wtr8
This thread proves that math sucks.
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Anonymous2007-02-22 23:03 ID:kjwB4oM4
>>50
This thread proves that the average person is not qualified to speak about math.
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Anonymous2007-02-23 14:34 ID:qwl1UYde
0.9999recurring is just a different string for the same value. it just so happens that the decimal number system is crude when it comes to representing such values
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Anonymous2007-02-23 15:50 ID:cjWS/YOi
>>52
There's nothing wrong with decimal. If you think there is something difficult about .999..., you just fail at math.
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Anonymous2007-02-23 16:36 ID:+STHOy9U
>>53
I'm not >>52
Although it should be noted that decimals are just estimations. The rational numbers can be expressed as a fraction, and the irrationals can generally be expressed by some infinite series and then estimated to the digits necessary.
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Anonymous2007-02-23 17:29 ID:PxOGa7sl
>>54
A decimal is not at all an estimation. Each one specifies a specific value. You can have a decimal specifying a value which ITSELF is an approximation (ie, 3.14159 ~= pi), but as I said, it is the value which is an approximation here, not the decimal - the decimal is specifying one single real number.
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Anonymous2007-02-23 19:05 ID:cjWS/YOi
>>55
Amen. All real numbers unambiguously represent a single quantity.
Not uniquely, though. That's the whole point of this topic.
The fact that this is the classic math troll has already been established. Kindly go fuck yourself.
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Anonymous2007-02-23 23:26 ID:MQuf7/CZ
>>55
A decimal is what thou dost experience with thine eye, but the number is not what thou dost experience with thine eye, but experience with thine mind.
BUT THE PROBLEM OCCURS CAUSE
1.000r = 0.999r + (1.000r-0.999r)
and 1.000r = 0.999r + (1.000r-0.999r) + (1.000r-0.999r) etc, onto infinity.
ALL NUMBERS ON THE REAL NUMBER LINE WELL END UP EQUAL TO EACH OTHER! SINCE EVERY REAL NUMBER IS EQUAL TO IT'S
INFINITELY CLOSE NEXT NUMBER, ETC.
I can't explain this well as I am not a mathematician, but real number line is epic fail!
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Anonymous2007-02-26 7:09 ID:beEuLrzo
Oh and to clarify my post, I know that 1.000r-0.999r is infinitely small, but what happens when you add an infintely small number an infinite amount of times....that's right every number on the real number line is equal to each other....cats and dogs living together!
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Anonymous2007-02-26 7:35 ID:beEuLrzo
1.000r = 0.999r so therfore 1.000r - 0.999r = 0
thus 1.000r = 0.999r + (1.000r-0.999r)
and 1.000r = 0.999r + 2 x (1.000r-0.999r), x3, x4, etc. onto eternity
BUT 1.000r = 0.999r + (1.000r-0.999r) x infinity
IF 1 / inifinty = 0, then 1.000r - 0.999r = 1 / infinity
SO 1.000r = 0.999r + infinity x (1 / infinity)
infinity x (1 / infinity), the infinities cancel out so you are left with 1 / 1
1.000r = 0.999r + 1 / 1
1 = 1.999r
1 = 2 WTF!!!!!!!!!!!
EVERY NUMBER ON THE REAL NUMBER LINE IS EQUAL TO EACH OTHER FAGGOTS!!!!!
Why the fuck is this thread still alive?
0.999.. = 1
End of fucking story. If you don't understand, go get a fucking education.
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Anonymous2007-02-26 21:56 ID:e7Jw2Rtp
infinity divided by infinity is a degenerate form and can equal anything because guess what, INFINITY IS NOT A NUMBER. It is a concept that is used to understand things. Here's a short and informal proof of why infinity is not a natural number:
For inifinity equals the largest natural number,
Let w equal the very largest number of the natural numbers. Add one to w. w < w + 1. Therefore w is not the largest number. Therefore, any "number" that could actually be larger than itself is not a natural number.
For your information: 0/0, infinity/infinity, 1^infinity, 0^0, infinity - infinity and a whole host of others are degenerate forms and can literally be ANY number.