what is division?
1 7
2 6
3 5
4 4
what is the concept of division?

what is division?
1 7
2 6
3 5
4 4
what is the concept of division?
Division can be seen as repeatedly subtraction of the denominator from the numerator. The result of the operation is how many times you can subtract the denominator from the numerator.
thyristor, that doesn't help explain (pi+1)/e easily. In general, a/b is defined to be the element x (if it exists) from what ever collection you are working in (groups, rings, graded algebra's etc) such that a = x * b
So 21/7 = 3 since 21 = 3*7
Sorry, I din't get what he meant by the sequence of numbers.
No idea either...
If it exists, it has to be unique as well – otherwise it’s not defined. 0/0 (in a field) is not defined because it’s not unique: 0 = 0·0 = 1·0.Originally Posted by river_rat
right and left divisors need not be unique though JaneBennet  you need a cancellation property usually for that to work if i recall.
And the cancellation property fails for 0 in a field because 0 does not have a multiplicative inverse in a field.
What I’m trying to say is
if b = 0, you cannot define a/b uniquely this way for the purpose of division. It would mean division by 0.a/b is defined to be the element x (if it exists) from what ever collection you are working in (groups, rings, graded algebras etc) such that a = x * b
I was heading more towards semigroups without cancellation where the zero problem explodes
consider the division 7/3. here if we subtract 3 from 7 repeatedly we reach a stage where the denominator is greater than the remainder.i. e. we obtain integers and fractions from division.
rofl jane bennet gets owned by river_rat every maths thread
The rat got mad mathematical skills
What for? Division makes less and less sense in that direction. If you’re explaining division (which is the point of this thread) you’re supposed to be heading in the opposite direction, towards division rings and fields – when the cancellation property holds (for nonzero elements).Originally Posted by river_rat
It's not a competition, dude.Originally Posted by organic god
Well for starters my masters is there so I like that area Semigroups are cool, and amazingly important and yet most people never see them until they pump into some serious analysis etc.Originally Posted by JaneBennet
Anyway, going to where division is better and better defined doesn't help you understand it (as you are using it already). You have to go somewhere where it doesn't work the way you are used to to get a grip on its implications.
Agreed. You stick with your semigroups, I’ll stick with my fields.Originally Posted by river_rat
Oh, doing research in field theory?
Totally.Originally Posted by organic god
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