# Math Help - if ab=ca, how to get b=c???

1. ## Re: if ab=ca, how to get b=c???

Originally Posted by Hartlw
For all a.

The examples were for a specific a.
The OP's original question began with "Let $a,b,c \in G$". That seems like the OP has a specific $a$, and is not looking for a condition where it will be true for all $a$. Perhaps the OP could clarify?

2. ## Re: if ab=ca, how to get b=c???

Originally Posted by SlipEternal
The OP's original question began with "Let $a,b,c \in G$". That seems like the OP has a specific $a$, and is not looking for a condition where it will be true for all $a$. Perhaps the OP could clarify?
Why did you wait till now to ask for a clarification of OP? It seems to have been accepted by everyone up till now.

Anyhow, have to leave for a long trip to my mother-in-law. Please do not interpret my silence as acquiesence to all the unfounded bloated obtuse objections.

3. ## Re: if ab=ca, how to get b=c???

The existence of an identity element does not contradict the above, as proposed in a disguised and obscured previous misguided post. Translated, the post says eb=ce →b=c without requiring G be commutative, which as an argument against commutatvity is of course nonsense. ae=ea is part of definition of a group. To add insult to injury, it was then suggested we ask OP how many elements in the group.
Another obfuscation, G generated by a, is irrelevant. G is either a group or it isn’t, and it has more elements than a (am≠a).

I used the definition of group to answer the OP, which seems to have generated a lot of confusion and/or nastiness. Perhaps the confused should look up the definition of a group.

There seems to be a conception among some that irrelevant and unnecessary abstraction is a sign of honesty and intelligence- on the contrary.

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