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..
The only time I've ever come across the modulo function is in computer programming. Is it much use anywhere else?
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.
do you think people will be allowed to make violins?
who's going to make the violins?
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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?
Everyone wants to change the world, noone wants to change himself.
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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