# Difference sign

Mathematical signs
arithmetic
Plus sign +
Minus sign - , ./.
Mark , ×
Divided sign : , ÷ , /
Plus minus sign ± ,
Comparison sign < , , = , , >
Root sign
Percent sign %
Analysis
Sum symbol Σ
Product mark Π
Difference sign , Nabla ,
Prime
Partial differential
Integral sign
Concatenation characters
Infinity symbol
geometry
Angle sign , , ,
Vertical , parallel ,
Triangle , square ,
Diameter sign
Set theory
Union , cut ,
Difference , complement ,
Element character
Subset , superset , , ,
Empty set
logic
Follow arrow , ,
Universal quantifier
Existential quantifier
Conjunction , disjunction ,
Negation sign ¬

The difference sign ∆ is a mathematical symbol derived from the Greek capital letter Delta . It was introduced by Leonhard Euler in 1755 together with the sum symbol ∑ derived from the Greek capital letter sigma . Johann I Bernoulli had previously suggested ∆ in another use.

## Typography and appearance

The glyph of the character is mostly identical to that of the Greek Δ, occasionally there are slight deviations (it is a little smaller in Linux Libertine ). The fact that especially in serif antiqua fonts the up and down strokes can be of different strengths is a special feature of the mathematical symbols that deal with a few characters that are also derived from letters ( sum symbols , product symbols, differential symbols ) and the typographically derived nabla Operator shares. In set theory it is therefore occasionally replaced as a symbol of symmetrical difference by a triangular symbol, the lines of which are all equally strong and which therefore harmonizes with other symbols of set theory in the design.

## use

### As a character

In texts with reference to numerical values, the character is occasionally found as an abbreviation for " difference ". To that extent it is also a character .

### In math

In mathematics the sign is used as:

### On desktop calculating machines

On desktop calculators , the symbol, usually in combination with the percentage symbol, is used to label the key for the inconsistently named function (e.g. "Calculation of percentage differences" or "percentage comparison") to calculate the percentage difference between two numbers entered immediately one after the other. In the same way, it is used to identify the result line on the protocol strip.

The input sequence results in: If 442 ∆% 479 =two digits after the decimal point are set, the result is "8.37", since 479 is 8.37% greater than 442 when rounded. With some models, two result lines are printed on the protocol strip: “37.00 ∆ ” (numerical difference, marked with the ISO 7000 symbol 0656 “Total” standardized “ ” after the difference symbol ) and “8.37 ∆%”.

## Representation on computer systems

The character is contained in Unicode as U + 2206 increment sign in the Mathematical Operators block , and in the Macintosh Roman character set at position CA hex .

## Individual evidence

1. ^ Hans Wußing , Lectures on the History of Mathematics , Verlag Harri Deutsch, Frankfurt am Main 1989 (reprint 2008), ISBN 978-3-817-11816-8 , p. 308.
2. ^ Leonhard Euler, Institutiones calculi differentialis , St. Petersburg 1755, vol. 1, p. 5, online in the Euler Archives of the Mathematical Association of America
3. Florian Cajori, A History of Mathematical Notations , Vol. 2, New York 1929, p. 265, reprint 2012, ISBN 978-0-486-67766-8 .
4. Olympia-Werke , Olympia CPD 5212 A - Operating Instructions , 1987, p. 5
5. TA Triumph-Adler Vertriebs GmbH, TA 1121 PD Carat - Operating Instructions , approx. 2002, p. 4