Show that zero is the identity for addition on R and 1 is the identity for multiplication on R. But there is no identity element for the operations `- : RxxR->R`and `-:: R_*xxR_*->R_*dot`

Explanation

To show that zero is the identity for addition on \( \mathbb{R} \) and that one is the identity for multiplication on \( \mathbb{R} \), as well as to demonstrate that there is no identity element for subtraction and division, we can follow these steps:

### Step 1: Show that 0 is the identity for addition on \( \mathbb{R} \)

1. **Definition of Identity Element**: An element \( E \) is called the identity element for a binary operation \( * \) if for every element \( A \) in the set, the following holds:
\[ A * E = A \quad \text{and} \quad E * A = A \]
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