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Two bars or three, and a modulus at the end of the line that decides everything.
Two horizontal bars is equality. Three is a congruence: a statement that two numbers leave the same remainder when divided by a modulus, and that modulus is written in brackets at the end of the line where it is the easiest thing on the page to overlook. Without the modulus the statement means nothing, and read as an ordinary equation it is simply false — which is why the extra bar matters more than its size suggests.
Two bars is equality; three is congruence, which depends on a modulus.
Drawn from the visual attributes recorded for each symbol. Only traits the two records disagree about are listed.
| Trait | Equals sign | Congruence sign |
|---|---|---|
| Orientation | orientation independent | upright |
| Equals sign | Congruence sign | |
|---|---|---|
| Bars | Two | Three |
| Claim | The two sides are the same | The two sides leave the same remainder, for a stated modulus |
| Depends on anything else | No | Yes — the modulus in brackets at the end of the line |
| Other uses of the glyph | Assignment in some programming languages | Definitions and identities elsewhere in mathematics |
| Relationship (from Symbolwise's records) | Commonly confused with Congruence sign — Two bars is equality; three is congruence, which depends on a modulus. | Commonly confused with Equals sign — Two bars is equality; three is congruence, which depends on a modulus. |
ISO 80000-2:2019, Quantities and units — Part 2: Mathematics
International Organization for Standardization · retrieved 2026-07-31
Paywalled and NOT READ for this batch. Registered so the standard can be named as existing and as covering mathematical signs; it supports no meaning in any record. See docs/paywalled-standards.md.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.
Two short parallel lines. Between atoms in a structural formula they are a double bond — two shared electron pairs. Between quantities they assert equality. There is no visual difference at all, and none is needed, because the two never appear in the same expression.
Count the horizontal strokes. One assigns a value. Two compare after converting types, which is where surprising results come from. Three compare without converting, so a string and a number are never equal. Miscounting is among the most common mistakes made by people new to the language, and nothing in the shape warns you.
Between two quantities, two level strokes assert that they are equal. Enclosed in a circle on a licensed work, the same two strokes are the no-derivatives condition: the work may be shared, but modified versions may not be distributed. Adapting it privately is not restricted — the condition is about sharing the result.
Alpha is a Greek letter and stands for a quantity — an angle, a coefficient, a significance level. The proportionality sign is an operator and stands between two quantities to say they keep a constant ratio. The drawings differ in that the proportionality sign's right-hand stroke runs out in an open curve rather than closing into the letter's tail.