Question

@Limitless @KingGeorge this is where the LaTeX will go as it doesn't work on chat.

Answer 1

\(\Large {1 \over n} \in \mathbb{R} :n \ne 0\)

Answer 2

Is this one correct?

Answer 3

Oh \(\cdots :n\ne 0,\infty\)

Answer 4

Your first was correct since \(\infty\notin\mathbb{R}\).

Answer 5

I see.

Answer 6

Two ways to define a function:

\[\begin{align}
f(x)&=\text{insert your expression in terms of } x\\
f:&X \to Y\\
&x \mapsto y
\end{align}\]
The second is under the condition that \(x\) is an element of \(X\) and \(y\) is an element of \(Y.\)

You mean to write
\[f(x)=\frac{1}{x} \,\,\, \{x: x \in \mathbb{R} \wedge x \ne 0\}.\]

Answer 7

@KingGeorge, \(\frac{1}{n}\in \mathbb{R}: n\ne 0\) is acceptable?

Answer 8

I meant to write that 1/n would be a real number if and only if n is not equal to infinity or zero/

Answer 9

You mean, then,
\[\left(\frac{1}{n} \in \mathbb{R}\right) \Leftrightarrow \left((n \ne 0) \vee (n \ne \infty)\right)\]
You may exclude the parentheses.

Answer 10

correct @Limitless \(\infty\) is not contained in the real numbers.

Answer 11

Your first post was correct, not the most recent one.

Answer 12

Interesting point, though. \(\mathbb{R}^{*}\) does consist of \(\infty\). It's called the extended real numbers. They are pretty cool.

Answer 13

@KingGeorge, I'm thinking I flubbed up the last part there. I think it should be \(\wedge\) instead of \(\vee.\) What do you think?

Answer 14

I heard that \(\mathbb{R}^*\) was supposed to be the non-zero real numbers?

Answer 15

It should be \(\wedge\), but really, it shouldn't be there since the second statement is meaningless anyways.

Answer 16

The lag has started. Let's insert the LaTeX only. REST TO CHAT.

Answer 17

Sorry, it should be \(\bar{\mathbb{R}}\) for the extended real numbers.

Answer 18

Also, \(^{*}\mathbb{R}\) is the hyperreal numbers.

Answer 19

\(\Large {1 \over x} \in \mathbb{R} : x \in \mathbb{R}^{*}\)

Answer 20

\[\{x: x\in \mathbb{R} \wedge x \ne 0\} \Rightarrow \frac{1}{x} \in \mathbb{R}\]

Answer 21

seems legit

Answer 22

\[S:=\left\{\frac{1}{x} :x\in \mathbb{R}^*\right\}\]

Answer 23

\(\Leftrightarrow, \Rightarrow, \Leftarrow.\) See how they are all (almost) the same length?\(\iff\) clashes horribly.

Answer 24

\(\Longleftarrow, \Longrightarrow, \Longleftrightarrow \). See how they are (almost) the same length? \(\Leftrightarrow \) clashes horribly.

Answer 25

\Leftrightarrow
\Leftarrow
\Rightarrow

\Longleftarrow
\Longrightarrow
\Longleftrightarrow

Why use more letters when you don't need to?