Question

note: e = is an element of...
For m e N(natural numbers), let Cm = {x e R(real numbers) | m - 1 <= x^2 < m}. Is C = {Cm | m e N(natural numbers)} a partition of R(real numbers)?

Answer 1

Quote: `jflush`
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note: e = is an element of...
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How cute!

Answer 2

Try using `\[ \]` and `\( \)` around math.

Answer 3

For \( m \in \mathbb{N} \) let \(C_m = \{x \in \mathbb{R} | m - 1 \le x^2 \lt m\}\). Is \(C = \{C_m | m \in \mathbb{N}\}\) a partition of \(\mathbb{R}\)?
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Answer 4

Okay so the real question is:
1) Is does every real number belong to some set in our partition?
\(\forall r\in \mathbb{R} \;\exists m\in \mathbb{N}: \;r\in C_m\)?
2) Does no real number belong to more than one set in our partition? \(\forall n,k\in \mathbb{N}\neg \exists r: r\in C_m\wedge r\in C_k\wedge m=k\)