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I want to convert a mathematics document to pdf, but I am getting missing $ errors.

Here is my code:

\documentclass{article}
\begin{document}
1. All prime numbers are odd

Universal Statement:
For all x \in \mathbb{N} such that for any a,b \in \mathbb{N}
x = ab where a or b must be equal to 1 and for any k \in \mathbb{N}, x = 2k + 1

Counterexample will comprise of:
A counterexample will be an x \in \mathbb{N} such that there exists a k \in \mathbb{N}
such that x = 2k

Counterexample:
2


6. For all real numbers x, we have x^2-2x+2 > 1

Universal Statement:
For all x \in \mathbb{R}, we have x^2-2x+2 > 1

Counterexample will comprise of:
A counterexample will be an x such that x^2-2x+2 < 1

Counterexample:
1


14. For all functions f : \mathbb{R} \rightarrow \mathbb{R}, if f is not increasing,
then it must be decreasing.

Universal Statement:
For all functions f : \mathbb{R} \rightarrow \mathbb{R} for all x_1, x_2 if
x_1 < x_2 and f(x_1) \ngeq f(x_2) then f(x_1) \leq f(x_2)

Counterexample will comprise of:
A counterexample will be a function f such that for all x_1, x_2 if x_1 < x_2 and
f(x_1) \ngeq f(x_2) then f(x_1) \nleq f(x_2)

Counterexample:
None, the statement is true

\end{document}

marked as duplicate by David Carlisle, Zarko, TeXnician, Kurt, user36296 Sep 24 '17 at 14:38

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  • 5
    surely it is clear that all the mathematics such as x \in \mathbb{N} should be in math mode? so $x \in \mathbb{N}$ and $x^2-2x+2 > 1$ etc – David Carlisle Sep 24 '17 at 13:54
2

What's the doubt? You never use $ in this document. For instance, insted of x \in \mathbb{N}, you should have written $x \in \mathbb{N}$ and instead of x^2-2x+2 > 1, you should have written $x^2-2x+2 > 1$.

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