Two a group is formed under any single operation like addition or multiplication. You have to define whether x is in the group under addition or multiplication. if it is under multiplication, then only you can apply cancellation law for multiplication.
What I am confused is that inorder to establish X-X=0, we don't need any grouping or anything like that. It is basic math. Once you establish that X-X=0, go back to your equation and substitute "0" wherever you have (x-x). There is one stage where you cancel (x-x) on LHS and RHS. There, what you are actually doing is stating 0/0=1. Which is not correct. There is no grouping required. For cancellation, number should not be a "0".
You need that. You can simply define X if you dont define its nature.
that ones true for sure.Thought that was just a rumor aunty.
Can you give me one example of any possible nature of X such that X-X=/=0 ? The fact is, You don't need to define the nature of X explicitly. The moment you write X-X, you have already defined it's nature.
You did not get my point.
@levina
Then the expression (X-X) becomes indeterminate, much like 0/0. It can't be 1 in any case. The "proof" you posted is very widely used. There was a connection to Ramanujam too (may be an urban myth). The correct identification of the fallacy is divide by zero. Check "/Mathematical_fallacy#Division_by_zero" in wiki. I am not denying that there are more methods to disprove that, but common method used is division by zero error.
That is exactly what i was saying. The operators like +, multiplication has to be defined in a group. Once you define those operators, then you can say that your set is a group under that operation with identity and inverse element. Since 0 is not present in I, the identity is 1 and inverse is 1/x for all x belongs to I and I is called as a group under multiplication. there x - x has no meaning. That prove which i used is a combination of both the group properties which can not be done simultaneously.
ha ha ha ha.
true!
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Cooking classes ....
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@levina anymore to cover in.......
hey. mera tuition fee do. itna padhaya. Pura group theory.true!
I had posted that thread sometime back
Ancient Computer Found In Roman Shipwreck
hmmm what about martial arts classes??
hu -ha!!
Errrr I'll think about it.
