Question

A binary operation \(\large * \) is defined on the set \(\large R \) of real numbers by \(\large x * y = \frac{x+y}{1+xy} \)

i. Determine whether or not \(\large * \) is associative

ii. Find the identity element \(\large e \)

Answer 1

What is associative?

Answer 2

a*(b*c)=(a*b)*c

Answer 3

yeah so check it :)

Answer 4

well i'm not putting it here to solve it myself lol, i want others to solve it so i see if i made mistakes...

Answer 5

it is asso...

Answer 6

but what is identity thingy?

Answer 7

Ishaan has corroborated!

Answer 8

<Element> <composition> <identity_element> = <Element> = <identity_element> <composition> <Element>

Answer 9

a*e=a

Answer 10

so you want something which satisfies x*e=x?

Answer 11

yeah

Answer 12

yes but that's incomplete definition saso.

Answer 13

Left identity and right identity element are unique

Answer 14

solve it then

x+e=e(1+xe)

Answer 15

(x+e)=x(1+xe)

Answer 16

0 is the identity element isn't?

Answer 17

ok well that's what i got.... 0 :D

Answer 18

Time to give me medal saso lol

Answer 19

Additional exercise find the inverse element.

Answer 20

i expected that lol, i just started typing the second question :P

Answer 21

x*e=1/x?

Answer 22

(x+e)x = (1+xe)
x^2 + ex =1 +xe
maybe i did something wrong