Do Thoughts Define Us?

It is often tempting to associate ourselves with our thoughts. Our mind is very active and thinks many things in the course of our day. If we analyze all these thoughts, we will likely find that many aren’t true.
For example, let’s say you are on a hike and see something glittering on the forest floor. You think, “wow! I must have found some lost jewelry,” only to discover upon closer inspection that it’s a crushed soda can. The initial thought wasn’t true, and it’s easy to reframe when you examine it more closely.
Here is some food for thought: if we actually believe that some of our thoughts aren’t true, how can they identify us?