Greater Than and Less Than Symbols (> < ≥ ≤): Meaning and How to Type Them

The greater than symbol (>) and less than symbol (<) compare two values: 7 > 3 says seven is greater than three, and 3 < 7 says three is less than seven. The open side of the symbol always faces the larger number and the point faces the smaller one.

This guide covers the comparison signs >, <, ≥, ≤, ≫, and ≪, the alligator trick for telling them apart, how to read and solve inequalities, and how to type every symbol on Windows, Mac, phones, HTML, code, and LaTeX.

Copy and Paste the Greater Than and Less Than Signs

• > — greater than (U+003E)
• < — less than (U+003C)
• ≥ — greater than or equal to (U+2265)
• ≤ — less than or equal to (U+2264)
• ≫ — much greater than (U+226B)
• ≪ — much less than (U+226A)
• ≯ — not greater than (U+226F)
• ≮ — not less than (U+226E)

The Greater Than and Less Than Symbols Explained

Both signs were introduced by Thomas Harriot in Artis Analyticae Praxis (1631); Pierre Bouguer added the "or equal to" versions in 1734.

The two basic symbols are mirror images, so orientation is all that matters:

• > opens to the left, so the left side is bigger: 10 > 2
• < opens to the right, so the right side is bigger: 2 < 10

The Alligator Trick

The classic way to remember the signs is to picture the symbol as a hungry alligator's (or crocodile's) open mouth. The alligator always eats the bigger number, so the mouth opens toward the larger value: in 8 > 5 and in 5 < 8 it is eating the 8 both times. A second cue: < looks like a tilted L, for "less."

Reading an Inequality Aloud

Read left to right, like an equation:

The ≫ ("much greater than") and ≪ ("much less than") signs have no precise threshold; physicists use them to justify approximations, as in "when v ≪ c, relativistic effects are negligible." The slashed ≯ and ≮ negate the basic signs.

Working With Inequalities

Number Lines and Interval Notation

An inequality in one variable describes a region on the number line: draw an open circle at the boundary for < and > (endpoint excluded) and a filled circle for ≤ and ≥ (endpoint included). Interval notation follows the same idea: x > 4 is (4, ∞), while x ≥ 4 is [4, ∞); round brackets exclude the endpoint and square brackets include it.

Compound Inequalities

Two conditions on one variable can be chained: −3 < x ≤ 5 means x is greater than −3 and at most 5, the interval (−3, 5]. Chains must point the same direction (2 < x > 7 is meaningless), and an "or" condition such as x < −1 or x > 1 stays as two statements.

Flipping the Sign

Adding, subtracting, or multiplying by a positive number leaves an inequality unchanged. Multiplying or dividing by a negative number reverses the sign:

• Start with −2x > 6
• Divide both sides by −2 and flip: x < −3

Check with x = −4: −2 × (−4) = 8, and 8 > 6 holds. Taking reciprocals of two positive numbers also flips the sign: 2 < 3 becomes 1/2 > 1/3.

How to Type Greater Than and Less Than Symbols

Windows: The basic > and < are on every keyboard. For ≥, hold Alt and type 242 on the numeric keypad; for ≤, use Alt + 243. These codes date from the original IBM PC code page and work in nearly every application. Word also accepts Alt + 8805 and Alt + 8804, or 2265 / 2264 followed by Alt + X.

Mac: Press Option + period for ≥ and Option + comma for ≤. For ≫ and ≪, use the Character Viewer (Control + Command + Space).

iPhone and Android: Tap 123, then #+= to reach > and <; press and hold > for ≥ and < for ≤.

HTML: A bare < begins a tag, so in web pages it must be escaped as < or the browser will read the text that follows as markup. A bare > is allowed, but > is the safe convention. The other signs are ≥, ≤, ≫, ≪, ≮, and ≯.

Comparison Operators in Programming

Every mainstream language uses the same four ASCII operators: <, >, <=, >=. Things to watch:

• The "or equal" forms put the equals sign second (<=, never =<); => in JavaScript and C# is an arrow function, not a comparison.
• Python allows chained comparisons (1 < x < 5); most other languages need x > 1 && x < 5.
• << and >> are bit shifts, not the ≪ and ≫ relations.

Greater Than and Less Than in LaTeX

The basic signs are typed directly as < and > in math mode; the rest are commands, with amssymb adding the negated and slanted variants:

```latex
\documentclass{article}
\usepackage{amsmath, amssymb}
\begin{document}
\[ 3 < 7, \qquad 7 > 3, \qquad x \leq 4, \qquad x \geq 4 \]
\[ -3 < x \le 5, \qquad -2x > 6 \implies x < -3 \]
\[ v \ll c, \qquad n \gg 1, \qquad a \nless b, \qquad a \ngtr b \]
\[ x \leqslant y, \qquad x \geqslant y, \qquad f(n) \lesssim g(n), \qquad f(n) \gtrsim g(n) \]
\end{document}
```

• \leq and \le are identical, as are \geq and \ge; \ll and \gg give ≪ and ≫.
• \nless, \ngtr, \nleq, and \ngeq (amssymb) give the slashed forms ≮, ≯, ≰, and ≱.
• \leqslant and \geqslant (amssymb) draw the slanted ⩽ and ⩾ preferred in many European texts.
• \lesssim and \gtrsim (amssymb) give ≲ and ≳, "less than or roughly equal to."

Write < and > only inside math mode: in text mode, pdfLaTeX with the default OT1 encoding prints ¡ and ¿ instead. Use \textless and \textgreater or $<$ and $>$.

Related Symbols

Which Way Does the Greater Than Sign Point?

The wide, open end faces the larger value and the point faces the smaller one. In 9 > 2 the opening is on the left, next to the 9.

What Does ≥ Mean?

"Greater than or equal to." The statement x ≥ 5 is true for 5 itself and for every number above 5; on a number line it gets a filled circle at 5, and in interval notation it is [5, ∞).

When Do You Flip an Inequality Sign?

Whenever you multiply or divide both sides by a negative number, or take reciprocals of two positive sides. Adding, subtracting, or scaling by a positive number never flips it.

Typesetting Inequalities That Look Right

Details like \leqslant versus \leq or a stray < in text mode can derail a document. Octree, the AI LaTeX editor at useoctree.com, writes correctly spaced comparison notation from a plain-language description and compiles it instantly. The full table of order relations with LaTeX commands is at https://tools.useoctree.com/symbols/order.