Asked by Amber
                i've got a question in my math
its wanting to know why is the 1 called the multiplicative identity
            
        its wanting to know why is the 1 called the multiplicative identity
Answers
                    Answered by
            Reiny
            
    multiplying any number by 1 does not change that number
e.g. 56x1 = 56
the number keeps its "identity".
BTW the "additive" identity would be the number 0
    
e.g. 56x1 = 56
the number keeps its "identity".
BTW the "additive" identity would be the number 0
                    Answered by
            Count Iblis
            
    The multiplicative identity is a number, denoted by 1 that has the property that:
1*x = x
for all x
You can then prove that there can only exist one number with this property. If you assume that there are two such numbers 1 and 1', then we have:
1*1' = 1'
because 1 is the identity.
But we also have:
1*1' = 1
because 1' is also the identity. So, we see that 1' = 1 and we see that the multiplicative identity is a unique number.
    
1*x = x
for all x
You can then prove that there can only exist one number with this property. If you assume that there are two such numbers 1 and 1', then we have:
1*1' = 1'
because 1 is the identity.
But we also have:
1*1' = 1
because 1' is also the identity. So, we see that 1' = 1 and we see that the multiplicative identity is a unique number.
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