Exploring Subsets: Understanding Integers and Their Relationships in Mathematics

[cragar]

This may be a dumb question but let's say i have the set of integers $\mathbb{z}$
can I say that $\frac{\pi}{\pi}$ or $(sin(x))^2+(cos(x))^2$
is a subset of the integers?

 

[chiro]

This may be a dumb question but let's say i have the set of integers $\mathbb{z}$
can I say that $\frac{\pi}{\pi}$ or $(sin(x))^2+(cos(x))^2$
is a subset of the integers?

The expression you gave (if I read the latex right) will always be 1. The set {1} will be a subset of Z if that is what you are asking.

 

[HallsofIvy]

No, 1 is member of the integers. {1} is a subset.

 

[cragar]

yes but the way we constructed 1 used numbers that are not part of the integers.
I don't know if that matters

 

[micromass]

yes but the way we constructed 1 used numbers that are not part of the integers.
I don't know if that matters

The way things are constructed doesn't matter. It's the final answer that will matter. So $\pi$ will not be a natural number, but $\pi/\pi$ will be, since the expression evaluates to 1, and that is all what matters.

 

[cragar]

ok thanks for your answer. I just wanted to be clear on it.