I thought it would be good if we had a board FAQ to explain basic concepts to the anonymii.
I'd start with:
1. Is it Maths or Math?
2. Is 1/0 infinite?
3. Is 0/0 i?
4. Is 0 positive?
5. Is 0.999999... equal to 1?
6. How did I do a barrel roll?
Name:
Anonymous2006-10-21 15:01
1- whichever
2- no
3- no
4- no
5- yes
6- with extreme skill
Name:
Anonymous2006-10-21 18:19
7. Is 0 a number?
Name:
Anonymous2006-10-21 18:21
7- yes
Name:
Anonymous2006-10-22 0:15
5. Only if you take as axiom that the decimal representation of a fraction of integers represents the limit of a process rather than the process itself. Which is what they teach these days, but you could make an alternate math system, it's A-OK. Every conclusion depends on what axioms are first defined as true.
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Anonymous2006-10-22 0:37
2. the limit of 1/0 is inf
Name:
Anonymous2006-10-22 0:47
>>5
That isn't an axiom, it's a consequence of the definition of the reals with Dedekind cuts. This definition isn't just "taught these days," it's the first formal definition of the real numbers and the one which has been accepted by academia for over a hundred years.
Name:
Anonymous2006-10-22 3:29
>>7
I'm not talking about real numbers per se silly, I'm talking about the numeral notation of what we call decimals, not the numbers that they are purported to represent.
Name:
Anonymous2006-10-22 4:43
That is to say, you can't talk Dedekind cuts with some kid who sees this for the first time. When a kid looks at 0.9999... he doesn't see a sequence that converges to a limit and then is defined to be that limit. It's not inherently implicit in the notation, but is learned to be recognised as such by those who study the subject. A kid is more likely to imagine a process that can't ever be completed, putting 9 after 9 after 9, as though by a long division gone horribly wrong. (The kid likely first encountered decimals with repeating digits when taught how to convert a fraction to a decimal by long division, and never produced 0.999... in the process.) When considered in terms understood by that kid, 0.999... will never get to the finish line. 0.999... is a shitty way to represent 1.
Name:
Anonymous2006-10-22 6:39
>>5
Yes, and in an alternate math system, 1+1=3. Your whole post is meaningless. I'd also like to point out that in standard decimal notation, 0.999... does not imply any process.
It's like you refuse to accept the standard real numbers simply because you *know* about other systems. Well guess what shithead, we know about them too, and in the absence of any mention of non-standard analysis, 0.999... = 1.
1. Maths in English, Math in drAterica.
2. Yes.
3. Yes.
4. It is neither positive or negative.
5. Yes.
6. gb2 /b/
Name:
Anonymous2006-10-22 19:54
>>13
The idea for this thread is that the questions are answered correctly.
Name:
Anonymous2006-10-22 23:32
>>10
You are incorrect. There is nothing inherent in the notation that reveals the meaning you abscribe to it. The association between notation and meaning is learned. I am not even talking about the real numbers and what they are (distinguish between the terms "number" and "numeral"), I'm talking about the symbolization and how people react to it based upon what they are taught or not taught about what it means. Your meaning for the notation is not covered in the people's first years of encountering it, assuming they ever go on to your level. You will never be successful explaining to a typical high school graduate what the hell you mean if all you can do is be insulting and ignore their experience and understanding of the notation, having to invoke concepts that essentially redefine for such people what the notation purportedly really means. You tell poor little Jeffy about Dedekind cuts some more, chief.
Your reply is odd, considering the closest thing posted that you could be replying to is this: "A kid is more likely to imagine a process..."
You are replying to something different or beyond what was actually posted.
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Anonymous2006-10-23 0:17
>>16
Ok, let me rephrase: Why not tell the kids that a decimal representation is not a process?
If you're going to go on and on about "the symbolization and how people react to it," you may as well not talk at all. Debating whether or not 0.999... = 1 without any sort of rigourous definition of what 0.999... and 1 mean is pointless and absurd. The question is a purely mathematical one, and the answer is that 0.999... = 1 unless someone specifies they are working in something other than the real numbers.
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Anonymous2006-10-23 5:44
sorry but 0.999... !=1. they have different numbers and 1-0.999... = 0.000..01 != 0 so they can't be the same.
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Anonymous2006-10-23 6:23
Well, this FAQ failed fast.
Name:
Anonymous2006-10-23 10:59
>>18
Right, an infinite number of zeroes followed by a one. Excellent logic.
Name:
Anonymous2006-10-23 16:16
2. 1/100=0.01, 1/100000= 0.00001, 1/0.00000000000000000001=100000000000000000000, go figure
3. Any number multiplied by 0 = 0, therefore 0/0 = any number
4. 0*-1=0, 0*1=0, therefore it is neither positive or negative
5. The 0.3333... you get from dividing 1 by 3 is just the way our decimal numerical system describes it. (1/3)*3=1 therefore 0.999999... = 1.
Name:
Anonymous2006-10-23 16:29
>>21
2. 1/-100=-0.01, 1/-100000= -0.00001, 1/-0.00000000000000000001=-100000000000000000000, go figure
3. it would be, but division doesn't return a set
Whichever. More precisely, Maths in English, Math in drAterica.
2. Is 1/0 infinite?
No, although the limit of 1/0 is infinite.
In any case, 1/100=0.01, 1/100000= 0.00001, 1/0.00000000000000000001=100000000000000000000, go figure.
3. Is 0/0 i?
No. Any number multiplied by 0 = 0, therefore 0/0 = any number.
4. Is 0 positive?
No, it is neither positive or negative.
5. Is 0.999999... equal to 1?
Yes, but only if you take as axiom that the decimal representation of a fraction of integers represents the limit of a process rather than the process itself. Which is what they teach these days, but you could make an alternate math system, it's A-OK. Every conclusion depends on what axioms are first defined as true. Then again, that isn't an axiom, it's a consequence of the definition of the reals with Dedekind cuts. This definition isn't just "taught these days," it's the first formal definition of the real numbers and the one which has been accepted by academia for over a hundred years.
That is to say, you can't talk Dedekind cuts with some kid who sees this for the first time. When a kid looks at 0.9999... he doesn't see a sequence that converges to a limit and then is defined to be that limit. It's not inherently implicit in the notation, but is learned to be recognised as such by those who study the subject. A kid is more likely to imagine a process that can't ever be completed, putting 9 after 9 after 9, as though by a long division gone horribly wrong. (The kid likely first encountered decimals with repeating digits when taught how to convert a fraction to a decimal by long division, and never produced 0.999... in the process.) When considered in terms understood by that kid, 0.999... will never get to the finish line. 0.999... is a shitty way to represent 1.
6. How did I do a barrel roll?
Pressing Z or R twice, with extreme skill, in /b.
7. Is 0 a number?
Yes.
8. Is 0.00000....01 = 0?
The number you are proposing is nonsensical. Go to the hyperreals.
No, the limit as x->0+ of 1/x is infinite. "The limit of 1/0" does not exist, because (surprise) 1/0 does not exist.
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Anonymous2006-11-01 14:09
What you talkin bout I see it right threre
Name:
Anonymous2006-11-01 15:03
>>30
Also note that infinity in that context is simply part of the definition of limits. That is, there is actually no separate concept of infinity, the whole construction is nothing more than an intuitive notation for 'as as x->0+, 1/x will keep growing'.
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Anonymous2006-11-03 1:29
Rule 99
Questions are answered like every other math question.
The limit of 1/0 exists if infinity has no sign :) See also Riemann sphere.
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Anonymous2006-11-03 21:42
>>35
The Riemann sphere isn't the real numbers, the complex numbers, or even a field, which is where this discussion is assumed to take place unless otherwise stated. You might as well say "1+1 = 5 because I'm working modulo 3 lawl."