Basic Arithmetic & Algebra Symbols

When starting to read math or quantitative formulas, the sheer number of symbols can be intimidating. However, many of these are just shorthand for English words you already know. Let's break down the most common ones.

Equality and Inequality

You are likely familiar with the equals sign, \(=\). But there are several related symbols:

(\neq) : Not equal to. Example: (5 \neq 3).
(≈) : Approximately equal to. Used when we round a number. Example: (\pi ≈ 3.14).
\(<\) : Less than. Think of it as an arrow pointing to the smaller number. Example: \(3 < 5\).
\(>\) : Greater than. Example: \(5 > 3\).
(\leq) : Less than or equal to. It combines the \(<\) and \(=\) symbols.
(\geq) : Greater than or equal to.

Basic Operations

Beyond basic addition (\(+\)), subtraction (\(-\)), multiplication ((\times) or (\cdot)), and division ((\div) or \(/\), or written as a fraction), you'll see:

(\pm) : Plus or minus. This means the number can be either positive or negative. For example, (\pm 5) means "+5 or -5".
(x^{y) : Exponents or Powers. This tells you to multiply (x) by itself (y) times. For example, (3}2 = 3 \cdot 3 = 9). We read this as "3 squared".
(\sqrt) : Square root. This asks "what number multiplied by itself gives (x)?" For example, (\sqrt{9} = 3) because (3 \cdot 3 = 9).

Variables and Constants

In algebra, letters are used to represent numbers.

Variables: Usually letters from the end of the alphabet like (x), (y), and (z). These represent unknown values that can change.
Constants: Usually letters from the beginning of the alphabet like (a), (b), and (c). These represent values that are fixed, even if we don't know exactly what they are right now.

There are also special constants that have a specific, unchanging value everywhere in math:

(\pi) (Pi): Approximately 3.14159. Used mostly in geometry and trigonometry.
(e) (Euler's Number): Approximately 2.718. It is extremely important in calculating continuous compound interest in finance.

Mini-Quiz

Question 1

What does the symbol (≈) mean?

Exactly equal to
Approximately equal to
Not equal to
Less than or equal to

Correct Answer: B Explanation: The symbol (≈) means "approximately equal to" and is typically used when values are rounded.

Question 2

How do you read the expression (4 \leq 5)?

4 is greater than 5
4 is equal to 5
4 is less than or equal to 5
4 is not equal to 5

Correct Answer: C Explanation: The (\leq) symbol combines the less than (\(<\)) and equals (\(=\)) symbols, meaning "less than or equal to".

Question 3

What does the constant (e) primarily represent in quantitative finance?

The square root of a negative number
Euler's number, used for continuous compounding
The ratio of a circle's circumference to its diameter
An unknown variable that can change daily

Correct Answer: B Explanation: Euler's number (\(e ≈ 2.718\)) is a mathematical constant that serves as the base of the natural logarithm, widely used for calculating continuous growth and compounding interest.