Explain whats wrong this statment above. Please help thank you
2007-05-05 14:49:21 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Because when the word identity is used without qualification it denotes something which is both a right-identity and a left-identity. Now, 1 has no problem with right-identity, because ∀x∈Q, x÷1 = x. However, it is not a left-identity for division, since 1÷x≠x (unless x=1 or x=-1). Therefore, 1 is not an identity element for division. 1 IS an identity element for multiplication, so perhaps that is what the statement should say.
2007-05-05 16:35:01 · answer #1 · answered by Pascal 7 · 1⤊ 0⤋
With the operation of multiplication, 1 is the identity element of the rationals because
1. 1 is in the rationals, and
2. for any x in the rational numbers, 1*x = x and x*1 = x.
Basically what's wrong with the statement is that it's not using the definition of the identity element to show 1 is the identity.
2007-05-05 15:18:02 · answer #2 · answered by blahb31 6 · 0⤊ 0⤋
instead of rational numbers it should say real numbers
2007-05-05 14:56:13 · answer #3 · answered by somethin_fierce 2 · 0⤊ 0⤋