Concept
0
Overview
0 (zero, ) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently dividing by 0 is generally considered to be undefined in arithmetic.
As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya.
Common names for the number 0 in English include zero, nought, naught (), and nil. In contexts where at least one adjacent digit distinguishes it from the letter O, the number is sometimes pronounced as oh or o (). Informal or slang terms for 0 include zilch and zip. Historically, ought, aught (), and cipher have also been used.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where 0 is discussed.
From (59), it follows that the system of equations (60) ∂F_{ρσ}/∂_x__{τ} + ∂F_{στ}/∂_x__{ρ} + ∂F_{τρ}/∂_x__{σ} = 0 is satisfied of which the left-hand side, according to (37), is an anti-symmetrical tensor of the third kind. This system (60) contains essentially four equations, which can be thus written:— { ∂F₂₃/∂_x₄_ + ∂F₃₄/∂_x₂_ ∂F₄₂/∂_x₃_ = 0 { { ∂F₃₄/∂_x₁_ + ∂F₄₁/∂_x₃_ ∂F₁₃/∂_x₄_ = 0 (60a) { { ∂F₄₁/∂_x₂_ +…
Albert Einstein, The Principle of Relativity
names the idea; states what it is; opens on it
I differentiate x and y, that is I consider x and y as being so infinitesimally small that they do not represent any real quantities, even the smallest, so that, of x and y nothing remains, except their reciprocal relations, a quantitative relation without any quantity; therefore dx/dy, the relation of the two differentials of x and y, is 0/0 but 0/0 is fixed as the expression of y/x. That this relation between two…
Friedrich Engels, Landmarks of Scientific Socialism
names the idea; states what it is; opens on it
TABLE 3/24. Digitalis purpurea. The tallest Flower-stem on each Plant measured in inches: 0 signifies that the Plant died, or did not produce a Flower-stem. Column 1: Number (Name) of Pot. Column 2: Plants raised from a Cross between different Flowers on the same Plant. Column 3: Plants raised from Flowers fertilised with their own Pollen. Pot 1 : 49 4/8 : 45 5/8.
Charles Darwin, The Effects of Cross & Self-Fertilisation in the Vegetable Kingdom
names the idea; states what it is
Primula auricula (Scott) : 80 : 15. Primula Sikkimensis (Scott) : 95 : 31. Primula cortusoides (Scott) : 74 : 66. Primula involucrata (Scott) : 72 : 48. Primula farinosa (Scott) : 71 : 44. Average of the nine species of Primula : 88.4 : 69. Hottonia palustris (H. Muller) : - : 61. Linum grandiflorum (the difference probably is much greater) : - : 69. Linum perenne : - : 20. Linum perenne (Hildebrand) : 0 : 0…
Charles Darwin, The Different Forms of Flowers on Plants of the Same Species
names the idea; opens on it
0.030 and 0.050; that for distinguishing one color from another was similarly 0.100 and 0.110; that for distinguishing a certain color from ten other colors, 0.105 and 0.117; that for distinguishing the letter A in ordinary print from the letter Z, 0.142 and 0.137; that for distinguishing a given letter from all the rest of the alphabet (not reacting until that letter appeared), 0.119 and 0.116; that for…
William James, Psychology
names the idea; opens on it
Related ideas
- French language
- Pingala
- Greece
- Princeton University Press
- Grapheme
- Glyph
- Hexadecimal
- Hinduism
- Anno Domini
- Zeno of Elea
- Integer
- Almagest
- Jainism
- Truth value
- Latin
- Fibonacci
- Propositional logic
- Indian mathematics
- Cosmology
- Ethiopia
- Middle Ages
- The Guardian
- Muslims
- Rational number
Opposing perspectives
Place in the tradition
Part of History of philosophy in Pakistan.