Hello all, I have an equivalence relation that I need some help with. Normally I find these to be fairly simple, however I'm not sure if I'm over-thinking this one or if it's just tricky.
For the relation: aRb $\Longleftrightarrow$ |a| = |b| on $\mathbb{R}$ determine whether it is an...
And the only reason it is $\mathbb{Z}^2$ and not $\mathbb{Z}$ is because there are two variables n and m, right? Because $\mathbb{Z}^2$ is shorthand for the Cartesian product, and this means $n$ belongs to $\mathbb{Z}$ and $m$ belong to $\mathbb{Z}$, which makes it squared. If there was only...
How do we know that it is non-negative? Couldn't m equal, say -2 and n equal -1?
Making the function $-1 \geq -4$ which would still be true, right?
I think I'm starting to understand. The notation used is just really throwing me off.
The range would be $\mathbb{Z}^+$ because (n, m) are...
A would be the set of all real numbers and B would be the set of all integers. Right?
Which would mean the first component of the ordered pair (for the Cartesian product) would be from $\mathbb{R}$
and the second component would be from $\mathbb{Z}$
I hope that's what you meant, otherwise I...
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Thank you for responding!
So, for the first one of yours:
A would be $\mathbb{R}$ and B would be in $\mathbb{Z}$?
Now if I have a function defined as
f: D -> $\mathbb{R}$ :: g((n, m)) = \[\sqrt{n-2m}\] with $D\subseteq $$\mathbb{Z}$$$^2$$
What would the range be? If I try what you...
Hello all, I'm having a lot of trouble when it comes to set notation.
For instance, what does (the set of all integers) $$Z^2$$ mean?
What values are contained in this set?Sorry if I didn't use the MATH tags right.