A number `a` is said to be congruent to `b` modulo `m` if `m` divides (a-b)
its written as a ≡ b mod m
so we can say that when we write a≡b mod m ,, `b` is the remainder that is obtained when` a` is divided by `m`.
now let us take a few examples:
but now u get this doubt, when 13 is divided by 4 , remainder is why only 1 ? why cant we say the remainder is -3 ????
infact this doubt is correct. we can even write
so we can write in various ways as we wish to..
I guess it would still require computer programming of some sort but Cryptology also makes extensive use of the mod function for coding. The RSA algorithm used in banking a prime example.
Last edited by Redbacks; 05-09-2010 at 09:38 PM.
big segment of algebra - i.e. group theory - is based on modular arithmetic (quotient groups and what not)
a big section of ring theory is as well. number theory too.
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Yes cryptography, and error-correcting codes (used in storage, data transmission networks) are all based on modulo arithmetic.
i might be wrong as it's been a while but i think error-correction/detection in cpu's work on churning stuff through polynomial rings? that's modular arithmetic.
What's the difference between an irrational number and a constant?
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Irrational number = you can't express that number as a fraction (like log 2).
A math Constant = a number that arises 'naturally' in math (like pi). A physical constant = a number that is somehow a fundamental part of nature (e.g, the gravitational constant).
There is overalp - pi is both irrational and a constant. It is also a transcendental number....
Hell, you can even say that pi is also a physical constant.
Last edited by silentstriker; 07-09-2010 at 12:44 PM.
Couldn't you say that all constants are irrational?
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