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> Zero, definition
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Dabeer
Posted: Nov 20 2010, 02:55 AM


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QUOTE (phyti @ Nov 19 2010, 09:53 PM)
It can't be that there is no next smaller number because by definition the real number line is continuous, there are no gaps.

You apparently don't understand what continuous means.

Read up at http://en.wikipedia.org/wiki/Linear_continuum

Specifically, note the following:

QUOTE (http://en.wikipedia.org/wiki/Linear_continuum)
For each x in S and each y in S with x < y, there exists z in S such that x < z < y


As rpenner stated, give me a number a and a claimed "next" number b and I will give you a number c, where c = (a+b)/2, that exists between a and b, thus proving that b is not the next number.


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phyti
Posted: Nov 21 2010, 11:50 PM


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Had to think about it for awhile, and after examining rpenners example for any errors, decided your response was the most appropriate.

"There is no such thing as a "next number"".

It just doesn't get more 'real' than that.
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Dabeer
Posted: Nov 22 2010, 11:59 PM


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QUOTE (RealityCheck @ Nov 22 2010, 04:59 PM)
What is the 'limit' value/number of 0.5r (or at least, of the 'series' that may be 'constructed' from it)?

In base 10, that would be 5/9

The rule is, take the repeating pattern and put it as the numerator with a denominator of an equal number of 9s. For other bases, use whatever digit is one less than the base. e.g. for base 3, use an equal number of 2s.

This post has been edited by Dabeer on Nov 22 2010, 11:59 PM


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"A denial of evolution - however motivated - is a denial of evidence, a retreat from reason to ignorance." - Dr. Tim D. White

"The problem with religion is that it is the only mode of thought that puts a positive value on a person's perpetual immunity to new evidence and new argument." - Sam Harris

"What a fool believes he sees no wise man has the power to reason away" - The Doobie Brothers
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waterpump
Posted: Nov 26 2010, 09:43 AM


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To return to the zero question - zero can also be regarded as the 'empty set', equally infinity can also be regarded as 'the full set'. So the infinity of integer number is 'all integer number'.

Note that in this case the infinity boundary is described as a 'quality of numberness', not a magnitude limit, the infinity boundary in this description represents a phase boundary or change of state - the ' (infinite) _quality_ of all integer numberness'. Mathematicians probably do not use this particular definition of infinity.

Please let me know.
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sporacle
Posted: Dec 9 2010, 06:04 AM


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Those numbers are slippery critters, represented by symbols we can type here. Perhaps there is an infinitely small one, indivisible, hiding next to zero. Hard to prove or falsify.
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boit
Posted: Mar 5 2013, 08:22 PM


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QUOTE (Dabeer @ Nov 10 2010, 06:47 PM)

Yes. It might help to think about it this way: in math, the precision is always absolute - in other words, 40 is really 40.0r. But when we write about these numbers, conveying ideas to one another, we just accept that the .0r part is implicit and save ourselves the trouble of writing it.



No, you're throwing the baby out with the bath water here. I agree that you have to have a correct concept of infinity to accept an infinitely repeating decimal, and that the concept of infinity might be purely theoretical - but the number itself is very real.



This just illustrates your lack of complete understanding of the real number line. There is no such thing as "exactly adjacent to". Give me any two non-equal numbers, no matter how small the difference between them, and I will be able to tell you a number that lies between them on the real number line. This is the basis for the challenge that I have repeated several times: if you think 0.3r is not exactly equal to 1/3, then give me the number x, such that 0.3r < x < 1/3. The challenge holds true for 0.9r and 1, as well.



Strictly speaking, this is not correct - there is a proper notation, and that is the ellipses "...". I do agree, however, that once all parties have mutually agreed that "r" will take the place of the ellipses, as we have implicitly done here by continuing to use it, then its use is perfectly acceptable.

Let's not hijack mik's thread guys. If you want to argue that 0.999 . . . or 0.9r is in fact 1 then come here.


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Boit was last taught physics in class way back in 1994. Whatever he's learnt thereafter is purely by personal effort through this forum and searching the net. He is not an authority in any matter science. Unless with clear referrence, what he puts forward is his own understanding of what he has read and may not always be correct. Peace.
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Derek1148
Posted: Mar 6 2013, 09:10 AM


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Edit. Didn't realize I was responding to a three year old post.

This post has been edited by Derek1148 on Mar 6 2013, 09:12 AM


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boit
Posted: Mar 6 2013, 11:05 AM


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QUOTE (Derek1148 @ Mar 6 2013, 12:10 PM)
Edit. Didn't realize I was responding to a three year old post.

Not that old. The new argument has started up in the Earth contracted diameter in Relativity Section. They have hijacked a thread to argue it.


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Boit was last taught physics in class way back in 1994. Whatever he's learnt thereafter is purely by personal effort through this forum and searching the net. He is not an authority in any matter science. Unless with clear referrence, what he puts forward is his own understanding of what he has read and may not always be correct. Peace.
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