Question

What does "identity" of a function mean?

Answer 1

This explains it well ; http://www.wolframalpha.com/input/?i=identity+function

Answer 2

an identity is like looking in the mirror--you see yourself

Answer 3

in addition, we have 0 as the identity; since a+0 = a

in multiplication, we have a as the identity; since a * 1 = a

Answer 4

an identity in general is defined as an element that when worked together with some operation, gives us back the same element:

f (operate) id = id (operate) f = f

Answer 5

Okay, now let * be a binary operation on set Q of rational numbers.
a*b =ab/4
Does this operation have an identity?

Answer 6

yes ...

a * i = ai/4 = a
therefore i/4 =1 when i=4

Answer 7

what about a*b = a (b)^2

Answer 8

can you determine an element i, such that a*i = i*a = a ?

Answer 9

1 ?

Answer 10

a(i)^2 = 1 ; if 1=1 or -1

i(a)^2 = a ; if i = 1/a

since there is no unique identity element for this, it is simply undefined/does not exist

Answer 11

pfft, a(i)^2 = a that is

Answer 12

So, because the "i" can be 1 or -1, identity does not exist?

Answer 13

correct, since i can be: 1, -1, or 1/a there is no unique element, i, that we can claim as THE identity element

Answer 14

Okay, but i dont get 1/a. a (i)^2=a will mean i^2 =1 right? Where did 1/a come from?

Answer 15

a * i ::has to equal:: i * a

the operation says, x*y is defined to be the first, multiplied by the square of the second.

a i^2 ::has to equal:: i a^2 in order for i to exist

Answer 16

\[i~a^2=a\]
\[i=\frac{a}{a^2}\]
\[i=\frac{1}{a}\]

Answer 17

Oh! Right. Now, I get it :)

Answer 18

I finally get the identity thing :D Thank you so much!! :)

Answer 19

youre welcome :)