# Math Help - algebraic properties of L(S)

1. ## algebraic properties of L(S)

The equation x^2-I=0 has infinitely many solutions on L(R).

Prove.

2. Originally Posted by bookie88
The equation x^2-I=0 has infinitely many solutions on L(R).

Prove.
What is $L(R)$? What do you mean by $x^2-I$? The first thing that comes to mind is $L^1(\mathbb{R} )$ and $x$ an operator $x:L^1(\mathbb{R} ) \rightarrow L^1 (\mathbb{R} )$. Am I right? Please give all the relevant definitions.

3. i figured it out. L(R) is linear equations of all real numbers.

so it would look like (a,b)^2-(1,0)=0
(a^2-1,ab+b)=0 and just solve from there.