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Greater Than or Equal To — Definition, Formula & Examples

Greater than or equal to means one number is either bigger than another number or exactly the same. The symbol for it is ≥.

For real numbers aa and bb, the statement a≥ba \geq b holds if and only if a>ba > b or a=ba = b. Equivalently, a≥ba \geq b means a−ba - b is zero or positive.

Key Formula

a≥ba \geq b
Where:
  • aa = The value that is at least as large as b
  • bb = The value that a is compared against

How It Works

The symbol ≥\geq combines two ideas: "greater than" (>>) and "equal to" (==). When you see x≥5x \geq 5, it means xx can be 5, 6, 7, or any number larger than 5. On a number line, you show this with a filled-in circle at 5 and a ray pointing to the right. The filled circle means 5 itself is included.

Worked Example

Problem: Is the statement 8 ≥ 3 true or false? What about 4 ≥ 4?
Check 8 ≥ 3: Ask: is 8 greater than 3, or equal to 3? Since 8 is greater than 3, the statement is true.
8>3⇒8≥3 is true8 > 3 \quad \Rightarrow \quad 8 \geq 3 \text{ is true}
Check 4 ≥ 4: Ask: is 4 greater than 4, or equal to 4? Since 4 equals 4, the statement is true.
4=4⇒4≥4 is true4 = 4 \quad \Rightarrow \quad 4 \geq 4 \text{ is true}
Answer: Both statements are true. Only one of the two conditions (greater than OR equal to) needs to hold.

Why It Matters

You encounter ≥\geq whenever a problem sets a minimum requirement. For instance, "you must be at least 48 inches tall to ride" translates to h≥48h \geq 48. In later courses like algebra and statistics, this symbol appears constantly in inequalities and interval notation.

Common Mistakes

Mistake: Confusing the direction of the symbol, writing 3≥83 \geq 8 when you mean 8≥38 \geq 3.
Correction: The open side of the symbol always faces the larger value. Think of ≥ as a mouth that wants to eat the bigger number.