The greater-than symbol > means the value on its left is greater than the value on its right. Read 7 > 4 as “seven is greater than four.” It is a strict comparison: the two sides cannot be equal.
How to read the greater-than sign
Read a comparison from left to right. In 9 > 6, the claim is that 9 is greater than 6, so the statement is true. Reversing the sides gives 6 > 9, which is false. The pointed end faces the smaller value, but the clearest way to check the sign is to say the complete relationship aloud.
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The sign compares values, not just individual numerals. In 3 + 4 > 6, evaluate the left expression first: 3 + 4 is 7, and 7 is greater than 6, so the comparison is true. Education Scotland’s numeracy and mathematics glossary defines it this way: “The symbol ‘>’ means greater than e.g. 7 > 4.” Education Scotland glossary.
Does greater than include the number itself?
No. The symbol > is strict, so a value equal to the boundary does not satisfy the comparison. For example, x > 3 allows values above 3 but excludes 3. By contrast, x ≥ 3 means x is greater than or equal to 3, so 3 is included. The New Zealand Ministry of Education illustrates the left-to-right reading with 5 > 4, meaning “five is greater than four” when read from left to right. New Zealand Ministry of Education learning resource.
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How it differs from related inequality symbols
Choose the symbol that matches the relationship between the two sides. In particular, use an inclusive symbol when equality is allowed.
| Symbol | Read as | Includes equality? |
|---|---|---|
> |
greater than | No |
< |
less than | No |
≥ |
greater than or equal to | Yes |
≤ |
less than or equal to | Yes |
For instance, if a condition allows a value of exactly 3, write x ≥ 3, not x > 3. Inequalities can describe a range of values and can also be shown on a number line.
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A quick way to check a comparison
-
Identify the value represented on each side. Evaluate any arithmetic expressions first.
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Read the statement aloud from left to right: “left side is greater than right side.”
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Check whether the claim is true, and decide whether equality should be allowed. If it should, use
≥rather than>.
The “open mouth faces the bigger number” mnemonic can help with orientation, but it is not a substitute for checking which side actually has the greater value.
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Where the notation came from
OpenStax reports that the first use of < and > for “less than” and “greater than” appeared in a mathematics book by English mathematician Thomas Harriot, published in 1631. OpenStax: Use the Language of Algebra.
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