1. Originally Posted by vcs
Basically the remainder of dividing one integer by another. For example 8 modulo 3 is 2.
Ah, thanks.

2. Originally Posted by andmark
Ah, thanks.
definition of congruent:

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:

9≡1mod2

13≡1mod4

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

13≡-3mod4

so we can write in various ways as we wish to..

3. The only time I've ever come across the modulo function is in computer programming. Is it much use anywhere else?

4. Originally Posted by Uppercut
The only time I've ever come across the modulo function is in computer programming. Is it much use anywhere else?
You could say time. with a 24 hour clock being mod 24 a general thing that people would use without thinking about it say when doing something in 30 hours.

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.

5. Originally Posted by Redbacks
You could say time. with a 24 hour clock being mod 24 a general thing that people would use without thinking about it say when doing something in 30 hours.

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.
Yeah, there is an entire branch of mathematics based on modulo arithmetic - rings, fields and groups all use modulo arithmetic if I'm not mistaken.

6. 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.

7. Originally Posted by Redbacks
You could say time. with a 24 hour clock being mod 24 a general thing that people would use without thinking about it say when doing something in 30 hours.

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.
I appreciated that, even if nobody else did.

8. Yes cryptography, and error-correcting codes (used in storage, data transmission networks) are all based on modulo arithmetic.

9. 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.

10. Originally Posted by Spark
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.
Yep..

11. Question:

What's the difference between an irrational number and a constant?

12. 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).

13. 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.

14. Couldn't you say that all constants are irrational?

15. And vice versa?

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