a) “Exponentiation on reals does not distribute over multiplication to the right.”
Hello thehollow89If there are two binary operations defined on a set , that are denoted by (say) and , then is right-distributive over if . So if represents exponentiation - in other words, - and represents multiplication - so - then
So exponentiation is right-distributive over multiplication.
If, however, to the right (which is a phrase I haven't come across in this context) means that the multiplication is on the right, then:
but
And these two are, of course, unequal. So this, if my interpretation is correct, is what the sentence 'Exponentiation does not distribute over multiplication to the right' means. (See PS.)
Note that this is similar to addition and multiplication, where
but .
So multiplication is right-distributive over addition, but (if my assumption about the use of the phrase 'to the right' is correct) multiplication 'does not distribute' over addition 'to the right'.
Maybe someone else on this Forum can confirm that my interpretation is correct?
Grandad
PS Alternatively, it could mean , which when compared to is again, not equal. So it is not distributive using this interpretation either. On reflection, I think this is the more likely meaning of 'exponentiation does not distribute over multiplication to the right'.