# Thread: Find a special set

1. ## Find a special set

Give a natural example of nonempty sets $X \subseteq Y$ with a common binary operation * where both X and Y have identity elements, but they are not the same.

Umm... I can't really think of anything, every set of integer mod would have 1 as identity...

2. Originally Posted by tttcomrader
Give a natural example of nonempty sets $X \subseteq Y$ with a common binary operation * where both X and Y have identity elements, but they are not the same.

Umm... I can't really think of anything, every set of integer mod would have 1 as identity...
Let $Y = \mathbb{Z}$ under multiplication. Note $1$ is the identity element for $Y$.
Let $X = \{ 0\}$ under multiplication. Note $0$ is the identity element for $X$.