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It's usually right but I wouldn't but much value on the implied importance Isaac Send a noteboard - 25/05/2010 04:22:52 PM
Yeah, that I can handle. Maybe I should delve a bit more to see what's actually going on but the notation is truly daunting for me. It's a bit like philosophy where you have to take a couple courses to define the terms before you can being the real study.


'Daunting Notation' in my experience stops being daunting as soon as people stop trying to memorize and absorb the notation and instead stop and ask 'why do they use this notation?', which is often where knowing the history of the field, especially that specific problem, tends to help - along with a vague knowledge of latin and greek usually. You're almost always, when learning a new math or physics tool, better off looking up the original problem it was meant to solve and trying to work it out yourself for a bit, until even though you haven't solved it you have a strong familiarity with what actually is the problem, then you look at the solution and suddenly the notation makes obvious sense. Take a previous modular arithmetic example. the whole 'modular' and 'modulus' bit in there is just using 'module' in the sense of individual piece with its own distinct importance. That modulus is all that really matters, it's distinct and relevant existence to the problem at hand is why you are even using the method. The notation is just an easier and clear way of writing it in general form. 14 = 2 (mod 12) is simply how you'd write in math notation 'The fourteenth hour of the day looks the same on a clock as the second hour, or the 26th or 38th or 50th.' Of course it would be kind of case specific to just write 14=2 (clock) or 17=10=3 (week) or 367=2 (year) all of which everyone would recognize instantly but would instead be written as 14=2 (Mod 12), 17=3 (Mod 7), and 367=2 (Mod 365)... most notation is like that, just common sense terminology agreed on to be easier to read, not confusable in context with something else, and general enough to be usable for non obvious examples.


Well, they're taking the position that 142857 is the only non-trivial case of a decimal without leading zeroes that repeats. Out of an infinite series of integers it seems to be in a class by itself.


That 'no leading zeroes' thing is sort of rubbish though. The reason nothing else has a cyclic behavior without a leading zero is because in base 10 it is impossible to divide 1 by any number bigger than 10 without getting 0.0XXXX, you can't get less than .1 without having a zero, and you obviously can't get a number bigger than .1 when your divisor is greater than 10. Plenty of numbers cycle, 1/81 cycles, it's just that 81 is bigger than 10 so in base 10 it has to have a zero following the radix point. (Decimal point is just the name for the base 10 radix point), so it's absurd to even say that out of an infinite series of integers none else cycle without a zero because only the 0-9 in decimal can produce a number whose reciprocal is greater than .1, it's unique value in that respect is purely an artifact of base 10
The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.
- Albert Einstein

King of Cairhien 20-7-2
Chancellor of the Landsraad, Archduke of Is'Mod
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Continuing the Math Theme, WTF Is Up with the Seven? - 25/05/2010 02:12:09 AM 649 Views
Base 10 number system - 25/05/2010 02:16:49 AM 486 Views
I Kinda Figured, but Why Does 7 Conflict with Base 10 So Much? - 25/05/2010 02:27:51 AM 477 Views
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Got me on a technicality. - 25/05/2010 09:19:54 AM 330 Views
Re: Got me on a technicality. - 25/05/2010 09:27:59 AM 369 Views
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You tend to get cyclic repeats when dividing by primes - 25/05/2010 11:58:34 AM 563 Views
I actually DO feel like taking a course on number theory. - 25/05/2010 12:12:10 PM 522 Views
Re: I actually DO feel like taking a course on number theory. - 25/05/2010 01:46:10 PM 364 Views
Well, I'm not vouching for Wikipedias claim, just reiterating it. - 25/05/2010 02:35:23 PM 581 Views
It's usually right but I wouldn't but much value on the implied importance - 25/05/2010 04:22:52 PM 426 Views
If you say so; I really try hard not to channel Pythagoras. - 26/05/2010 09:26:22 AM 594 Views
Re: If you say so; I really try hard not to channel Pythagoras. - 26/05/2010 10:00:37 AM 541 Views
The "leading zero" thing IS a bit misleading. - 26/05/2010 11:06:59 AM 673 Views
Re: The "leading zero" thing IS a bit misleading. - 26/05/2010 12:33:08 PM 396 Views
i have a book you're welcome to try reading.... - 26/05/2010 07:30:46 AM 357 Views
Yeah, I keep getting much that impression. - 26/05/2010 09:07:41 AM 338 Views
Why is 6 afraid of 7? *NM* - 25/05/2010 02:15:59 PM 187 Views
There it is again! Because 7 is a gluttonous beast. - 25/05/2010 02:27:58 PM 400 Views

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