Exploring Math and Logic in Markdown with KaTeX

Representing Mathematical Concepts with KaTeX

With KaTeX integration, we can now write beautiful mathematical formulas using LaTeX syntax directly in our Markdown.

Basic Arithmetic and Algebra

Inline formulas like $a + b = c$ or $x^2 + y^2 = z^2$ are rendered neatly.

For display mode (block) formulas, use double dollar signs:

The Quadratic Formula

Here is the quadratic formula rendered with KaTeX:

An Integral Example

And an example of an integral:

Inline Examples with Symbols

• The Greek letter pi is $\pi$.
• A square root: $\sqrt{x}$.
• Approximately equal: $a \approx b$.
• Not equal: $x \neq y$.
• Greater than or equal to: $N \ge 0$.
• Less than or equal to: $P \le 1$.
• Summation: $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$
• Fractions: $\frac{1}{2}$

Logical Statements

Representing logical operations and statements also benefits from LaTeX syntax for symbols if desired, though plain text or Unicode often suffice.

• AND: $P \land Q$ (or P && Q)
• OR: $P \lor Q$ (or P || Q)
• NOT: $\neg P$ (or !P)
• IMPLIES: $P \Rightarrow Q$ (or P -> Q)
• IF AND ONLY IF (IFF): $P \Leftrightarrow Q$ (or P <-> Q)

Example of a Logical Argument (using text):

1. If it is raining ($P$), then the ground is wet ($Q$). ($P \Rightarrow Q$)
2. It is raining ($P$).
3. Therefore, the ground is wet ($Q$).

This can be written as:

Premise 1: P ⇒ Q
Premise 2: P
Conclusion: Q

KaTeX integration significantly improves the presentation of mathematical and symbolic content, making it more accessible and professional.