Equals sign

The equals sign (British English) or equal sign (American English), also known as the equality sign, is the mathematical symbol =, which is used to show when two things are the same or equal. In math, it is placed between two expressions that have the same value. For example, in the equation 2 + 2 = 4, the equals sign tells us that both sides of the symbol have the same result.

This important symbol was invented in 1557 by the Welsh mathematician Robert Recorde. He chose it because he believed that no two things could be more equal than the two lines that make up the symbol. Today, the equals sign is used all around the world in math, science, and many other areas where we need to show that two values or ideas are the same.

In computers, the equals sign has a special code called a code point, which is U+003D in systems like Unicode and ASCII. This helps computers recognize and use the symbol correctly in different programs and languages.

History

Before the 16th century, people did not have a common symbol for equality. Instead, they used words like aequales or gleich to show that two things were the same. One of the earliest uses of a symbol for equality was by Diophantus around AD 250, who used a special Greek letter.

The symbol we use today, =, was invented in 1557 by the Welsh mathematician Robert Recorde in his book The Whetstone of Witte. Recorde chose two parallel lines because he believed nothing could be more equal than two lines of the same length. At first, this symbol was not popular and was not used again until 1618. It became widely accepted in the 1600s, especially after famous mathematicians like John Wallis, Isaac Barrow, and Isaac Newton used it, helping it spread across Europe.

There were other symbols for equality used around the same time. For example, in 1559, a French monk named Johannes Buteo used a different symbol, and in 1571, Wilhelm Xylander used two parallel vertical lines. Even the famous mathematician René Descartes used a different symbol in his book in 1637. However, Recorde's symbol eventually became the standard because it was used by key thinkers in mathematics.

Usage in mathematics and computer programming

In math, the equals sign shows that two things are the same. For example, you might see "x = 2," meaning x is equal to 2. It can also be used to define something, like saying "let x = 2," or to make conditions, such as "if x = 2, then…"

In computer programming, the equals sign is used in different ways. The first programming language to use it was Fortran in 1957. In Fortran, X = 2 means to set the value of X to 2. Another language, ALGOL, used the equals sign to check if two things are equal, like in if x = 2.

Today, many languages use = for setting values, while others use it to check for equality. Some languages, like JavaScript, use == to check equality and === for checking both value and type. For example, in PHP, 0 == false is true, but 0 === false is false because they are different types.

Other uses

The equals sign is used in many different ways beyond math. In some African languages such as Budu and Dan, it serves as a tone letter to show pronunciation.

In names, the equals sign has been used to connect parts of a double-barreled name. For example, the aviation pioneer Alberto Santos-Dumont sometimes used it instead of a regular hyphen.

In language studies, the equals sign marks where a small word called a clitic attaches to another word.

In chemistry, the equals sign is used to represent chemical bonds. Two lines side by side show a double bond between atoms.

The equals sign has also become a symbol for equal rights, especially for the LGBT community. It has been used since 1995 by groups like the Human Rights Campaign and the United Nations Free & Equal to show support for equal treatment.

In old communication methods like telegrams and Telex, the equals sign was used to separate parts of a message. In Morse code, it is represented by the letters B and T put together.

Related symbols

See also: Unicode mathematical operators and Glossary of mathematical symbols § Equality, equivalence and similarity

Approximately equal

Main article: Approximation § Typography

There are special symbols to show when things are almost the same but not exactly equal. Some of these symbols include:

• ≈ (U+2248 ≈ ALMOST EQUAL TO, LaTeX \\approx)
• ≃ (U+2243 ≃ ASYMPTOTICALLY EQUAL TO, LaTeX \\simeq)
• ≅ (U+2245 ≅ APPROXIMATELY EQUAL TO, LaTeX \\cong)
• ∼ (U+223C ∼ TILDE OPERATOR, LaTeX \\sim)
• ∽ (U+223D ∽ REVERSED TILDE, LaTeX \\backsim)
• ≐ (U+2250 ≐ APPROACHES THE LIMIT, LaTeX \\doteq)
• ≒ (U+2252 ≒ APPROXIMATELY EQUAL TO OR THE IMAGE OF, LaTeX \\fallingdotseq)
• ≓ (U+2253 ≓ IMAGE OF OR APPROXIMATELY EQUAL TO, LaTeX \\risingdotseq)

Not equal

The symbol to show when things are not equal is ≠ (U+2260). In computer programming, different symbols like !=, /=, or <> are used instead.

Identity

The triple bar symbol ≡ (U+2261, LaTeX \\equiv) is used to show that two things are exactly the same or equal by definition.

Isomorphism

The symbol ≅ is used to show that two shapes or structures are the same in form.

In logic

Different symbols can be used to show that two ideas or statements have the same truth value.

In geometry

The symbol ≏ (LaTeX \\bumpeq) is used to show that two directed line segments have the same length and direction.

Other related symbols

There are many other special symbols related to equality in Unicode, including:

• ≌ (U+224C ≌ ALL EQUAL TO)
• ≔ (U+2254 ≔ COLON EQUALS)
• ≕ (U+2255 ≕ EQUALS COLON)
• ≖ (U+2256 ≖ RING IN EQUAL TO)
• ≗ (U+2257 ≗ RING EQUAL TO)
• ≘ (U+2258 ≘ CORRESPONDS TO)
• ≙ (U+2259 ≙ ESTIMATES)
• ≚ (U+225A ≚ EQUIANGULAR TO)
• ≛ (U+225B ≛ STAR EQUALS)
• ≜ (U+225C ≜ DELTA EQUAL TO)
• ≞ (U+225E ≞ MEASURED BY)
• ≟ (U+225F ≟ QUESTIONED EQUAL TO)
• ⩴ (U+2A74 ┮ DOUBLE COLON EQUAL)
• ⩵ (U+2A75 ⩵ TWO CONSECUTIVE EQUALS SIGNS)
• ⩶ (U+2A76 ⩶ THREE CONSECUTIVE EQUALS SIGNS)

Incorrect usage

The equals sign is sometimes used the wrong way in math problems, especially by students who are just learning. For example, when adding the numbers 1, 2, 3, 4, and 5, someone might write:

1 + 2 = 3 + 3 = 6 + 4 = 10 + 5 = 15.

This looks like a shortcut for writing many equations together, but it is not correct. Each part of this chain has a different total, so it cannot all be equal. A better way to show the steps is:

1 + 2 = 3,
3 + 3 = 6,
6 + 4 = 10,
10 + 5 = 15.

This mix-up happens because the equals sign can mean two different things. In early math classes, it often means "the answer is..." like pressing the equals button on a calculator. In algebra, it means two things are truly the same. This confusion can continue even in college.

Encodings

The equals sign is a special symbol used in math. It shows that two things are the same or equal. In computers, it has a special code called U+003D.

There are also other symbols that are related to the equals sign, like the “not equal to” sign and many more.