7 Shocking Secrets Of The Greater Than And Less Than Signs (< And >) You Never Learned In School

Every student learns them early, but few grasp the true depth and power of the greater than (>) and less than (<) signs. These simple V-shaped symbols, which define one of the most fundamental concepts in mathematics—the concept of order—are far more than just elementary school mnemonics. As of December 12, 2025, their role has expanded dramatically, moving from basic arithmetic to becoming the bedrock of modern programming, advanced data filtering, and complex machine learning algorithms. This article will reveal the seven most surprising facts about the inequality symbols, from their 17th-century origin to their critical function in today's digital world.

The Surprising History and Evolution of the Inequality Symbols

The symbols we use daily to compare numbers are surprisingly modern inventions in the grand timeline of mathematics, a field thousands of years old. The history of the greater than and less than signs is a fascinating journey from a private manuscript to a universal standard.

• Originator: Thomas Harriot (1560–1621)
• Nationality: English
• Primary Field: Mathematics, Astronomy (worked on the telescope before Galileo)
• First Appearance: Posthumously published in his 1631 work, Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas (The Analytical Arts Applied to Solving Algebraic Equations).
• The Non-Strict Symbols: The familiar "greater than or equal to" ($\ge$) and "less than or equal to" ($\le$) symbols were not introduced until over a century later.
• Introduction of $\ge$ and $\le$: The French mathematician Pierre Bouguer first used these symbols in 1734, originally using a single line beneath the inequality sign (e.g., $\frac{>}{=}$).

Secret #1: They Were Invented by a Man Who Mapped the Moon

The credit for inventing the $\gt$ and $\lt$ symbols belongs to the brilliant, yet largely unsung, English mathematician and astronomer, Thomas Harriot. Harriot was a polymath who made significant contributions to algebra and optics. He was one of the first people to draw a map of the Moon through a telescope—even before Galileo—and his work on algebraic notation was revolutionary. The symbols were only published in 1631, ten years after his death, in his book on analytical arts. This delay meant their adoption was slow, but their elegant simplicity eventually won out, cementing Harriot's legacy in every math classroom worldwide.

Secret #2: The Alligator Mnemonic is Mathematically Sound

For generations, students have been taught the mnemonic device that the inequality sign acts like a hungry alligator or crocodile, its open mouth always facing the larger number. While this analogy is simplistic, it perfectly captures the core mathematical concept: the symbol always "points" to the smaller value and "opens" to the greater value. This concept of *relational operators* is fundamental, establishing a clear order between two quantities.

The Digital Dominance: Inequality Signs in Programming and Data Science

In the 21st century, the greater than and less than signs have transcended mathematics to become essential tools in computer science, forming the basis of *Boolean logic* and conditional statements.

Secret #3: They Are the Gatekeepers of Code

In almost every programming language—from Python and Java to C++ and JavaScript—the $\gt$ and $\lt$ symbols are known as *comparison operators* or *relational operators*. Their primary function is to evaluate a relationship between two values and return a Boolean result: either `True` or `False`.

• Conditional Logic: They are the core of `if` statements, controlling the flow of a program. For example, `if (score > 90): print("Pass")` is a comparison that determines whether a block of code is executed.
• The Combined Operators: In coding, the non-strict inequalities are written by combining the comparison operator with the equals sign:
  • `>=` (Greater than or equal to)
  • `<=` (Less than or equal to)

This simple True/False evaluation is the engine that drives complex software, from video games to financial trading algorithms.

Secret #4: The Critical Role in Data Filtering and Analysis

In the world of *data science* and *machine learning*, these signs are indispensable for filtering and managing massive datasets. Data scientists use them in languages like Python and R to create subsets of data, a process known as *data slicing*. For instance, when analyzing clinical data, researchers frequently encounter values that are outside the measurable range of an instrument—known as the *limits of quantification*. These values are often reported using inequality signs, such as `<250 mgdl` or `>2500 mg/dL`, indicating the true value is beyond the measurable limit. Furthermore, in machine learning, they are conceptually important in techniques like *log transformation*, which helps normalize data by making ratios less than 1 and greater than 1 more symmetrical.

Advanced Applications and Common Confusion

While their basic use is straightforward, the inequality signs are central to advanced mathematical concepts, particularly when dealing with infinite sets and complex algebraic reasoning.

Secret #5: The Key to Unbounded Sets and Interval Notation

In higher-level mathematics, especially *algebraic reasoning* and calculus, the signs are used to define the boundaries of a solution set. This is where the concept of *interval notation* comes into play. The strict inequality signs ($\gt$ and $\lt$) correspond to open intervals, which are represented by parentheses ( ) in interval notation, meaning the endpoint is *not* included in the solution. The non-strict signs ($\ge$ and $\le$) correspond to closed intervals, represented by square brackets [ ], meaning the endpoint *is* included. The ultimate use of the signs in this context is defining an *unbounded set*—a range of numbers that extends infinitely in one direction. For example, the statement $x > 5$ is written in interval notation as $(5, \infty)$, where the infinity symbol ($\infty$) is always paired with a parenthesis because infinity is not a number that can be "equal to" or included.

Secret #6: The Hidden Meaning in HTML and XML

For web developers, the less than sign ($\lt$) and greater than sign ($\gt$) have a special, non-mathematical function: they serve as the crucial delimiters for *HTML* and *XML* tags. Every tag, such as `

` for a paragraph or `` for an image, must begin with $\lt$ and end with $\gt$. Because of this, when a programmer wants to display the actual symbols on a webpage without the browser interpreting them as code, they must use special *HTML entities* to prevent a rendering error:

• &lt; is used to display the `<` sign.
• &gt; is used to display the `>` sign.

This dual role highlights how a simple mathematical symbol can become a foundational element of global digital infrastructure.

Secret #7: Solving Compound Inequalities is More Complex Than You Think

A common point of confusion, even for advanced students, is the *compound inequality*, which combines two or more inequality statements. * The "AND" Inequality: When you see a statement like $5 < x < 10$, it is shorthand for a conjunction: $x$ is greater than 5 AND $x$ is less than 10. The solution must satisfy both conditions simultaneously. * The "OR" Inequality: For instance, a statement like $x < 5$ or $x > 10$ defines a set of numbers that is *disjoint* (separated). Mastering the use of these symbols in *linear inequalities* and *set builder notation* is a hallmark of strong *algebraic reasoning*, proving that the simple angle shape is the gateway to complex mathematical thought. From the 17th-century calculations of Thomas Harriot to the conditional logic of modern artificial intelligence, the greater than and less than signs remain one of the most powerful and versatile symbols ever conceived.