- #1

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For example: <a+b>*<c+d> = ? or <a+b>^2=?

Here, <> is the fractional part, i.e <4.2> = 0.2

There is plenty I could find on mod N arithmetic with n>1 but nothing on mod 1.

thanks for any tips.

Svensl

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- Thread starter svensl
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- #1

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For example: <a+b>*<c+d> = ? or <a+b>^2=?

Here, <> is the fractional part, i.e <4.2> = 0.2

There is plenty I could find on mod N arithmetic with n>1 but nothing on mod 1.

thanks for any tips.

Svensl

- #2

AKG

Science Advisor

Homework Helper

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- #3

- #4

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With modulo N arithmetic I was referring to:

http://en.wikipedia.org/wiki/Modular_arithmetic for example.

If N=12 as in hour clock system, I could say that (13 mod 12)*(14 mod 12) = 2 = ((13*14) mod 12) = 2. This I meant by simplification. However, these rules do not work for cases for mod 1. So, (1.222 mod 1)*(5.111 mod 1) is not equal to ((0.222*0.111) mod 1). I was wondering whether there are rules for this sort of thing.

For example, I can write <a + b > = <<a>+<b>>. Again <> stands for mod 1.

Or, <-a> = 1 - <a>.

Are there any for multiplication?

thanks,

svensl

- #5

uart

Science Advisor

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If N=12 as in hour clock system, I could say that (13 mod 12)*(14 mod 12) = 2 = ((13*14) mod 12) = 2. This I meant by simplification. However, these rules do not work for cases for mod 1. So, (1.222 mod 1)*(5.111 mod 1) is not equal to ((0.222*0.111) mod 1).

Yes but it's not the difference between "1" and "12" that's operating here, it's the far more fundamental difference that in one case you're doing modulo arithmetic over the integers and in the other case you're doing it over the reals.

Try doing modulo 12 arithmetic over the reals and see how many of those results still hold.

- #6

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Do you know of any literature which talks about mod 1? There is a wealth of literature on equidistributed mod 1 sequences, number theory, ergodic theory......but I have not found helping me whith my problem.

Cheers,

svensl

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