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Tamazight NLP 24

RSA and Diffie–Hellman use modular exponentiation.

“ⵔ,ⵙ,ⴰ” ⴷ “ ⴷⵉⴼⵉ ⵀⵉⵍⵎⴰⵏ” ⵙⵎⵔⵙⵏ ⴰⴳⴳⴰⴹ ⴰⵏⴰⵡⴰⵢ.

It is used by the most efficient implementations of polynomial greatest common divisor, exact linear algebra and Gröbner basis algorithms over the integers and the rational numbers.

ⵉⴽⴽⴰⵜ ⴷⴰ ⵉⵜⵜⵓⵙⵎⵔⴰⵙ ⴳ ⵜⵣⵎⵔⵜ ⵏ ⵓⵎⴱⴹⵓ ⵏ ⵓⵎⵙⵙⵓⵔ ⴰⵅⴰⵜⴰⵔ ⵉⵍⴰⵏ ⴽⵉⴳⴰⵏ ⵏ ⵉⵡⵜⵜⴰ ⴷ ⵍⵊⵉⴱⵔ ⴰⵡⵏⵖⴰⵏ ⴰⵎⵏⵖⵓⴷ ⴷ “ⴰⵍⴳⵓⵔⵉⵜⵎ” ⵏ ⴳⵔⴰⵏⴰⵔⴰ ⵖⴼ ⵉⵎⴹⴰⵏ ⵉⵎⴷⴷⴰⴷⵏ ⴷ ⵡⵓⵟⵟⵓⵏ ⵓⵎⴳⵉⵏⴻⵏ.

The modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context.

ⴳ ⴽⵉⴳⴰⵏ ⵏ ⵜⵓⵜⵍⴰⵢⵉⵏ ⵏ ⵓⵙⵖⵉⵡⵙ ⴷ ⵉⵎⴰⵙⵙⵏ ⵏ ⵓⵙⵙⵉⵟⵏ, ⵜⴳⴰ ⵜⵉⵙⵏⵙⵉ ⵏ ⵓⵙⵙⵉⵟⵏ ⴰⵏⴰⵡⴰⵢ ⵉⵜⵜⵓⵙⵎⵔⴰⵙⵏ ⴽⵉⴳⴰⵏ ⴳ ⵓⵙⴰⵜⴰⵍ ⴰⴷ.

The method of casting out nines offers a quick check of decimal arithmetic computations performed by hand.

ⴷⴰ ⵜⵙⴽⴰⵔ ⵜⴱⵔⵉⴷⵜ ⵏ ⵓⵙⵙⵓⴼⵖ ⵏ ⵜⵥⴰ ⵏ ⵜⴰⵔⴽⵉⵡⵉⵏ; ⴰⵣⵣⵔⴰⵢ ⵓⵔⵎⵉⴹ ⴰⵙⵉⴹⵏ ⵉ “ⵜⵙⵙⵉⵟⵏⵜ ⵜⴰⵎⵔⴰⵡⵜ” ⵏⵏⴰ ⵉⵜⵜⵓⵢⴰⴳⴰⵏ ⵙ ⵓⴼⵓⵙ.

A linear system of congruences can be solved in polynomial time with a form of Gaussian elimination, for details see linear congruence theorem.

ⵉⵖⵢ ⴰⴷ ⵉⵜⵜⵓⴼⵙⴰⵢ ⵓⵏⵎⴰⵍⴰ ⴰⵎⵙⴰⵙⴰ ⴰⵡⵏⵖⴰⵏ ⴳ ⵜⵉⵣⵉ ⵎⵎ ⵉⵡⵜⵜⴰ ⵙ ⵢⴰⵜ ⵜⴰⵍⵖⴰ ⴳ ⵜⴰⵍⵖⵉⵡⵉⵏ ⵏ “ⴳⵓⵙⵢⴰⵏ”, ⵎⴰⵔ ⴰⴷ ⵜⴰⴽⵣⴷ ⵓⴳⴳⴰⵔ ⵉⵣⵉⵕ “ ⵜⴰⵎⴰⴳⵓⵏⵜ ⵏ ⵓⵎⵙⴰⵙⴰ ⴰⵡⵏⵖⴰⵏ”.

The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is defined by a systematic generalization of this basic definition.

ⴷⴰ ⵉⵜⵜⵓⵙⵉⵙⵙⵏ ⵓⵙⴼⵜⴰⵢ ⵏ ⵉⵎⴹⴰⵏ ⵉⵎⴷⴷⴰⴷⵏ ( ⴳ ⵍⵍⴰⵏ ⴰⵡⴷ ⵡⵓⵟⵟⵓⵏ ⵓⵣⴷⵉⵔⵏ), ⴷ ⵉⵎⴹⴰⵏ ⵓⵎⴳⵉⵏⴻⵏ (ⵉⵎⵜⵡⴰⵍⵏⴻⵏ), ⴷ ⵡⵓⵟⵟⵓⵏ ⵏ ⵜⵉⴷⵜ ⵙ ⵓⵙⵎⴰⵜⴰ ⵉⵙⵏⵎⴰⵍⴰⵏ ⴰⵙⵓⵙⵙⵏ ⴰⴷ ⴰⴷⵙⵍⴰⵏ.

The product of two measurements is a new type of measurement.

ⵜⴰⵢⴰⴼⵓⵜ ⵏ ⵓⴽⴼⵓⴷ ⵏ ⵙⵉⵏ ⵉⵙⵖⴰⵍⵏ ⴰⵢⴷ ⵉⴳⴰⵏ ⵢⴰⵏ ⵡⴰⵏⴰⵡ ⴰⵎⴰⵢⵏⵓ ⵏ ⵓⵙⵖⴰⵍ.

The inverse operation of multiplication is division.

ⵜⵉⵎⴳⴳⵉⵜ ⵏ ⵓⴽⴼⵓⴷ ⴰⵎⵓⵖⵓⵍ ⴰⵢⴷ ⵉⴳⴰⵏ ⵜⵉⴱⴹⵉⵜ.

The division of a number other than 0 by itself equals 1.

ⵜⵓⴱⴹⵓⵜ ⵏ ⵉⵎⵉⴹ ⵙ ⵓⵎⵣⵉⵔⴰⵢ ⵏ “0” ⴷⴰ ⵉⵜⴳⴳⴰ “1”.

This implicit usage of multiplication can cause ambiguity when the concatenated variables happen to match the name of another variable, when a variable name in front of a parenthesis can be confused with a function name, or in the correct determination of the order of operations.

ⵉⵖⵢ ⴰⴷ ⵉⵙⴽ ⵓⵙⵙⵎⵔⵙ ⵓⴼⴼⵉⵔ ⵏ ⵓⴽⴼⵓⴷ ⴰⵡⵍⴰⵍⵍⴰⵙ, ⵉⴳ ⵎⵛⴰⵛⴽⴰⵏⵜ ⵜⵎⵙⴽⵉⵍⵉⵏ ⵜⵉⵙⵏⴽⵓⴷⴰⵏⵉⵏ ⴰⴽⴷ ⵢⵉⵙⵎ ⵏ ⵓⵎⵙⴽⵉⵍ ⵏⵏⵉⴷⵏ, ⴰⴷⴷⴰⵢ ⵏⵉⵖⵉ ⴰⴷ ⵏⵙⵙⵓⵔ ⵉⵙⵎ ⵏ ⵓⵎⵙⴽⵉⵍ ⴷⴰⵜ ⵜⴰⵙⴽⵉⵡⵜ ⴷ ⵢⵉⵙⵎ ⵏ ⵜⵏⴰⵎⴽⵜ, ⵏⵖⴷ ⴳ ⵢⵉⴽⵉⵣ ⴰⵎⴷⴷⴰⴷ ⵏ ⵓⵙⵙⵓⴷⵙ ⵏ ⵜⵉⴳⴳⵉⵡⵉⵏ.

"The numbers to be multiplied are generally called the ""factors""."

ⵓⵟⵟⵓⵏ ⵏⵏⴰ ⵔⴰⴷ ⵉⵜⵜⵓⴽⴼⵓⴷⵏ ⵙ ⵓⵎⴰⵜⴰ ⴰⵢⴷ ⵉⴳⴰⵏ “ ⵉⵎⵎⴰⴽⵏ”.

"Also as the result of a multiplication does not depend on the order of the factors, the distinction between ""multiplicand"" and ""multiplier"" is useful only at a very elementary level and in some multiplication algorithms, such as the long multiplication."

“ ⴷ ⴰⵡⴷ ⵜⴰⵢⴰⴼⵓⵜ ⵏ ⵓⴽⴼⵓⴷ ⵓⵔ ⴷⴰ ⵜⵙⴽⵓⵜⵜⵓ ⵖⴼ ⵓⵙⵙⵓⴷⵙ ⵏ ⵡⴰⵎⵎⴰⴽⵏ, ⴷⴰ ⵉⵜⴳⴳⴰ ⵓⵙⵏⵓⵃⵢⵓ ⴳⵔ “ ⵓⵙⴼⵜⴰⵢ” ⴷ “ⵓⵎⵙⴼⵜⴰⵢ” ⵓⴱⵖⵉⵔ ⴷⴰⵢ ⴳ ⵓⵙⵡⵉⵔ ⴰⵎⵣⵡⴰⵔⵓ ⴽⵉⴳⴰⵏ, ⴷ ⵉⵜⵙⵏⵜ “ⴰⵍⴳⵓⵔⵉⵜⵎ ⵏ ⵓⴽⴼⵓⴷ” ⴳ ⵢⵉⴳⴳⵉⵜⵏ ⵉⵖⵣⵣⴰⴼⵏ ⵏ ⵓⴽⴼⵓⴷ”.

The result of a multiplication is called a product.

ⵜⴰⵢⴰⴼⵓⵜ ⵏ ⵓⴽⴼⵓⴷ ⴰⵢⴷ ⵉⴳⴰⵏ ⴰⴼⴰⵔⵙ.

The slide rule allowed numbers to be quickly multiplied to about three places of accuracy.

ⴷⴰ ⵜⵜⴰⴷⵊⴰ ⵜⵍⴳⴰⵎⵜ ⵏ ⵓⴼⵙⵙⵓⴳⴰⵏ ⴰⴷ ⵉⵙⴼⴼⵓⴽⵜⵉ ⵓⵟⵟⵓⵏ ⵙ ⵣⵔⴰⴱⵉⵜ ⴰⵔ ⴰⵜⵜⴰⵢⵏ ⵏ ⴽⵕⴰⴹ ⵉⴷⵖⴰⵕⵏ ⵙ ⵜⵙⴷⴷⵉ.

The general theory is given by dimensional analysis.

ⴷⴰ ⵜⵜⵓⴼⴽⴰ ⵜⵎⴰⴳⵓⵏⵜ ⵜⴰⵏⵎⴰⵜⵜⴰⵢⵜ ⵙ ⵜⵙⵍⵟ ⵏ ⵡⵓⴳⴳⵓⴳⵏ.

The complex numbers do not have an ordering.

ⵉⵎⴹⴰⵏ ⵓⴷⴷⵉⵙⵏ ⵓⵔ ⵍⵉⵏ ⴰⵙⵏⵎⴰⵍⴰ.

Here we have identity 1, as opposed to groups under addition where the identity is typically 0.

ⴷⴰⴷⵖ ⵖⴰⵔⵏⵖ ⵜⴰⵎⴰⴳⵉⵜ 1, ⵓⵔ ⵉⴷ ⵣⵓⵏⴷ ⵜⵉⵔⴰⴱⴱⵓⵜⵉⵏ ⵏ ⴷⴷⴰⵡ ⵜⵔⵏⵓⵜ ⴳ ⵡⴰⵍⴰ ⵜⴳⴳⴰ ⵜⵎⴰⴳⵉⵜ 0.

To see this, consider the set of invertible square matrices of a given dimension over a given field.

ⵎⴰⵔ ⴰⴷ ⵜⴰⵏⵏⴰⵢⴷ ⵖⴰⵢⴰ, ⴳ ⵖ ⵓⵙⵡⵉⵏⴳⵎ ⵏⵏⴽ ⵜⴰⵔⴱⵉⵄⵜ ⵏ ⵉⴷⵔⴰⵙⵏ ⵉⵎⴽⴽⵓⵥⵏ ⵉⵍⴰⵏ ⵜⵓⴹⵓⵜ ⵎⵎ ⵡⵓⴳⴳⵓⴳ ⴰⵎⵥⵍⴰⵢ ⴳ ⴽⴰⵏ ⵢⵉⴳⵔ.

Another fact worth noticing is that the integers under multiplication is not a group—even if we exclude zero.

ⵜⵍⵍⴰ ⵜⵉⴷⵜ ⵢⴰⴹⵏ ⵙ ⵉⵍⴰⵇ ⴰⵙ ⵏⴽ ⵜⴰⵖⴹⴼⵜ ⵏⵏⴰ ⵉⴳⴰⵏ; ⵉⵎⴹⴰⵏ ⵉⵎⴷⴷⴰⴷⵏ ⴷⴷⴰⵡ ⵓⵙⴼⵓⴽⵜⵉ ⵓⵔ ⵉⴳⵉⵏ ⵜⴰⵔⴱⵉⵄⵜ ⵎⵇⵇⴰⵔ ⴰⵙⵏ ⵏⴽⵙ ⴰⵎⵢⴰ.

"In mathematics, a percentage (from Latin per centum ""by a hundred"") is a number or ratio expressed as a fraction of 100."

ⴳ ⵜⵓⵙⵏⴰⴽⵜ, ⵜⵉⴳⵎⵉⴹⵉ (ⵙⴳ ⵜⵉⴳⵎⵉⴹⵉ ⵜⴰⵍⴰⵜⵉⵏⵉⵜ “ ⵙ ⵜⵎⵉⴹⵉ”) ⵜⴳⴰ ⵓⵟⵟⵓⵏ ⵏⵖⴷ ⴰⵙⵖⵍ ⵉⵍⴰⵏ ⴰⵡⵏⵏⵉ ⴰⵎⵜⵡⴰⵍ ⵏ 100.

Computation with these fractions was equivalent to computing percentages.

ⵉⴽⴽⴰⵜ ⵓⵙⵙⵉⵟⵏ ⵙ ⵉⵎⵜⵡⴰⵍⵏ ⴰⴷ, ⵉⴳⴰ ⵜⵉⴳⵎⵉⴹⵉ ⵏ ⵜⵎⵙⵙⵉⵟⵏⵜ.

Whenever communicating about a percentage, it is important to specify what it is relative to (i.e., what is the total that corresponds to 100%).

ⵉⴳ ⴷⴰ ⵏⵙⴰⵡⴰⵍ ⵖⴼ ⵜⵉⴳⵎⵉⴹⵉ ⵉⵇⵏⴻⵏ ⴰⴷ ⵏⵙⵙⵉⴽⵣ ⵎⴰⵢⴷ ⵉⴳⴰⵏ ⴰⵙⵖⵍ (ⵉ.ⴻ., ⴰⵎⵙⵎⵓⵏ ⵉⵎⵙⴰⵙⴰⵏ ⴷ 100%).

"When speaking of a ""10% rise"" or a ""10% fall"" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity."

“ⵉⴳ ⴷⴰ ⵏⵙⴰⵡⴰⵍ ⵖⴼ “”ⵓⵔⵏⵓ ⵏ ⵓⵙⵖⵍ 10%” ⵏⵖⴷ “ⵓⴳⵓⵣ ⵙ ⵓⵙⵖⵍ 10%” ⴳ ⵜⵎⴰⴽⵜⴰ, ⴰⵙⵙⴼⵔⵓ ⵉⵍⵍⴰⵏ ⵉⴳⴰⵜ; ⴰⵢⴰ ⵉⵍⴰ ⵜⴰⵣⵍⵖⴰ ⵙ ⴰⵜⵉⴳ ⴰⵎⵣⵡⴰⵔⵓ ⵏ ⵜⵎⴰⴽⵜⴰ ⵏⵏⴰ.

The same confusion between the different concepts of percent(age) and percentage points can potentially cause a major misunderstanding when journalists report about election results, for example, expressing both new results and differences with earlier results as percentages.

ⵉⵖⵢ ⴰⴷ ⵉⵙⵙⴽⵔ ⵡⵓⵛⵓⵔ ⵏⵏⴰⵖ ⴳⵔ ⵉⵔⵎⵎⵓⵙⵏ ⵉⵎⵣⴰⵔⴰⵢⵏ ⵉ ⵜⵉⴳⵎⵉⴹⵉ (ⴰⵡⵜⴰⵢ) ⴷ ⵜⵏⵇⵇⴰⴹ ⵙⴳ ⵜⵉⵎⵉⴹⵉ ⴳ ⴳⴰⵔ ⴰⵔⵎⵎⵓⵙ ⵎⵇⵇⵓⵔⵏ ⴰⴷⴷⴰⵢ ⵙⴽⵔⵏ ⵉⵙⵏⵖⵎⴰⵙⵏ ⴰⵙⵉⵡⴹ ⵖⴼ ⵜⴼⵔⵏⵉⵏ, ⵙ ⵓⵎⴷⵢⴰ; ⴰⵙⵉⵡⵍ ⵖⴼ ⵜⵢⴰⴼⵓⵜⵉⵏ ⵜⵉⵎⴰⵢⵏⵓⵏ ⴷ ⵓⵎⵣⵉⵔⴰⵢ ⵏ ⵜⵉⴳⵎⵉⴹⵉ ⴰⴽⴷ ⵜⵢⴰⴼⵓⵜⵉⵏ ⵉⵣⵔⵉⵏ.

The term has been attributed to Latin per centum.

ⵉⵙⵓⵏⵏⴹ ⵉⵔⵎ ⵖⵔ ⵜⵉⴳⵎⵉⴹⵉ ⵜⴰⵍⴰⵜⵉⵏⵉⵜ.

Grammar and style guides often differ as to how percentages are to be written.

ⴳ ⴽⵉⴳⴰⵏ ⵏ ⵜⵉⴽⴽⴰⵍ ⴷⴰ ⵜⵎⵣⴰⵔⴰⵢⵏ ⵡⵓⵎⵍⴰⵏ ⴷ ⵉⵍⴳⴰⵎⵏ ⴷ ⵡⴰⵎⵎⴰⴽ ⴳ ⵎⴰⵢⴷ ⵉⵥⵍⵉⵏ ⵙ ⵜⵎⴰⵎⴽⵜ ⵏ ⵜⴰⵔⴰⵢⵜ ⵏ ⵜⴳⵎⵉⴹⵉⵡⵉⵏ.

"When interest rates are very low, the number 0 is included if the interest rate is less than 1%, e.g. ""% Treasury Stock"", not ""% Treasury Stock"".)"

ⴰⴷⴷⴰⵢ ⴳⵣⵏ ⴽⵉⴳⴰⵏ ⵡⴰⵜⵉⴳⵏ ⵏ ⵓⴱⵖⵓⵔ ⴷⴰ ⵉⵜⵜⵓⵔⵏⵓ ⵓⵟⵟⵓⵏ 0, ⵎⴽ ⵜⴽⴽⴰ ⵜⵢⴰⴼⵓⵜ ⵏ ⵓⴱⵖⵓⵔ ⴷⴷⴰⵡ 1%, ⵙ ⵓⵎⴷⵢⴰ “% ⵏ ⵓⵢⴷⴷⴰ ⵉⵍⵍⴰⵏ ⴳ ⵉⵣⵖⵉ” ⵓⵔ ⵉⴷ “% ⵏ ⵓⵢⴷⴷⴰ ⵉⵍⵍⴰⵏ ⴳ ⵉⵣⵖⵉ”.

Likewise, the winning percentage of a team, the fraction of matches that the club has won, is also usually expressed as a decimal proportion; a team that has a .500 winning percentage has won 50% of their matches.

ⵣⵓⵏⴷ, ⵜⵉⴳⵎⵉⴹⵉ ⵏ ⵓⵎⵓⵔⵙ ⴳ ⵜⵔⴰⴱⴱⵓⵜ, ⴷ ⴽⴰ ⴳ ⵉⵎⵃⵉⵣⵡⴰⵔⵏ ⵏⵏⴰ ⵢⵓⵡⵢ ⵓⵙⵔⵉⵔ, ⴷⴰ ⵖⵉⴼⵙ ⴰⵡⴷ ⵏⵙⴰⵡⴰⵍ ⵙ ⵜⵉⴳⵎⵔⴰⵡ, ⵜⴰⵔⴰⴱⴱⵓⵜ ⵎⵉ ⵢⵓⵡⴹⵏ ⵓⵙⵖⵍ ⵏ ⵡⴰⵔⵔⴰⵣ ⵏⵏⵙ 500 ⵀⴰⵜ ⵉⵔⵣⴰ ⵙ ⵓⵙⵖⵍ ⵏ 50% ⴳ ⵉⵃⵎⵣⵡⵓⵔⵏ ⵏⵏⵙ.

Subtraction also obeys predictable rules concerning related operations, such as addition and multiplication.

ⵜⵍⴰ ⴰⵡⴷ ⵜⵓⴽⵙⴰ ⵉⵍⴳⴰⵎ ⵙ ⵉⵖⵢ ⴰⴷ ⵉⵙⵏⵉⵎⴰⵍ ⴳ ⵎⴰⵢⴷ ⵉⵥⵍⵉⵏ ⵙ ⵉⵎⴳⴳⵉⵜⵏ ⵉⵍⴰⵏ ⵜⴰⵣⵍⵖⴰ, ⵣⵓⵏⴷ ⴰⵎⴰⴳⵓⵜ ⴷ ⵓⵙⴼⵓⴽⵜⵉ.

Performing subtraction on natural numbers is one of the simplest numerical tasks.

ⵜⵉⴳⴳⵉ ⵏ ⵜⵓⴽⵙⴰ ⵖⴼ ⵉⵎⴹⴰⵏ ⵉⵖⴰⵔⴰⵏⴻⵏ ⴰⴷ ⵉⴳⴰⵏ ⵉⵎⵙⴽⴰⵔⵏ ⵉⵎⴹⴰⵏ ⵉⵡⵀⵏ.

Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend.

ⵙ ⵜⵓⵏⵚⵉⴱⵜ ⵉⴳⴰ ⵡⵓⵟⵟⵓⵏ ⵉⵜⵢⴰⴽⵙⵏ ⴷⴰ ⵉⵜⵙⵎⵎⴰ ⴰⵎⵢⴰⴽⴽⴰⵙ, ⵎⴰⴽⴰ ⵓⵟⵟⵓⵏ ⴷⵉⴽⵙ ⵉⵜⵢⴰⴽⴽⴰⵙⵏ ⴰⵢⴷ ⵉⴳⴰⵏ ⴷⴷⵓⵣⴷⴰⵔ.

"Subtraction"" is an English word derived from the Latin verb subtrahere, which in turn is a compound of sub ""from under"" and trahere ""to pull""."

“ⵙⵓⴱⵙⵜⵔⴰⴽⵛⵏ” ⵢⴰⵜ ⵜⴳⵓⵔⵉ ⵜⴰⵏⴳⵍⵉⵣⵉⵢⵜ ⴷ ⵉⴼⴼⵖⵏ ⵙⴳ ⵓⵎⵢⴰⴳ ⴰⵍⴰⵜⵉⵏⵉ “ⵙⴰⴱⵜⵔⵀⵉⵔ”, ⵉⴳⴰⵏ ⵓⴷⴷⵉⵙ ⵏ “ⵙⴰⴱ” ⵙⴳ “ⴰⵏⴷⵔ” ⴷ ⵜⵓⴹⴼⵕⵜ ⵏ “ ⵜⵓ ⴱⵓⵍ”.

From position 3, it takes no steps to the left to stay at 3, so .

ⵙⴳ ⵓⵙⵓⵔⵙ 3, ⵓⵔ ⵉⵔⵉ ⵡⴰⴷⴷⴰⴷ ⴰⵡⴷ ⵢⴰⵜ ⵏ ⵜⵙⵓⵔⵉⴼⵉⵏ ⵖⵔ ⴰⵥⵍⵎⴰⴹ ⵎⴰⵔ ⴰⴷ ⵏⵇⵇⵉⵎ ⴷⴰⵔ 3, ⵖⵎⴽⴰⵏⵏ.

To represent such an operation, the line must be extended.

ⵎⴰⵔ ⴰⴷ ⵏⵙⵎⴷⵢⴰ ⵣⵓⵏⴷ ⵜⵉⵎⴳⴳⵉⵜ ⴰⴷ, ⵉⵇⵏⴻⵏ ⵓⵍⴷⴰⵢ ⵏ ⵉⵣⵔⵉⵔⵉⴳ.

"The leading digit ""1"" of the result is then discarded."

“ ⴰⴽⴽⵓⴷⵍ ⵏ ⵡⵓⵟⵟⵓⵏ “1” ⵙⴳ ⵜⵢⴰⴼⵓⵜ.

In the ten's place, 0 is less than 1, so the 0 is increased by 10, and the difference with 1, which is 9, is written down in the ten's place.

ⴳ ⵜⵓⵣⵓⵏⵜ ⵏ ⵜⵉⵎⵔⴰⵡⵉⵏ, 0 ⵜⴷⵔⵓⵙ ⵅⴼ 1, ⵅⴼ ⵓⵢⴰ 0 ⴷⴰ ⵉⵜⵜⵓⵔⵏⵓ ⵙ ⵓⵙⴳⵯⵔ ⵏ 10, ⴷ ⵓⵎⵣⵉⵔⴰⵢ ⴷ 1 ⵉⴳⴰⵜ 9, ⵉⵜⵢⴰⵔⴰ ⴳ ⵜⵓⵣⵓⵏⵜ ⵏ ⵜⵉⵎⵔⴰⵡⵉⵏ.

The subtraction then proceeds in the hundreds place, where 6 is not less than 5, so the difference is written down in the result's hundred's place.

ⴹⴰⵕⵜ ⵓⵢⴰ ⴷⴰ ⵜⵜⵓⵙⴽⴰⵔ ⵜⵎⴳⴳⵉⵜ ⵏ ⵜⵓⴽⴽⵙⴰ ⴳ ⵜⵓⵣⵓⵏⵜ ⵏ ⵜⵉⵎⴰⴹ, ⴰⴷ ⵓⵔ ⵉⴽ ⵡⴰⵜ ⵏ 6 ⴷⴷⴰⵡ ⵡⵉⵏ 5, ⵄⴰⴷ ⵉⵜⵢⴰⵔⴰ ⵓⵎⵣⵉⵔⴰⵢ ⴳ ⵜⵓⵣⵓⵏⵜ ⵏ ⵜⵉⵎⴰⴹ.

Rather it increases the subtrahend hundred's digit by one.

ⴷ ⴷⴰ ⵜⵜⵉⵍⵉ ⵜⵎⵔⵏⵉⵡⵜ ⵉ ⵡⵓⵟⵟⵓⵏ ⴰⵎⴰⴽⵙ ⵙ ⵓⵙⴳⵯⵔ ⵏ ⵢⴰⵏ.

The answer is 1, and is written down in the result's hundred's place.

ⵜⴰⵎⵔⴰⵔⵓⵜ ⵜⴳⴰ 1, ⴷ ⵜⵢⴰⵔⴰ ⴳ ⵜⵓⵣⵓⵏⵜ ⵏ ⵜⵉⵎⴰⴹ.

This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin.

ⵜⵡⴰⴳⴰ ⵜⴰⵖⴰⵍⵜ ⵏ ⵜⵎⴰⴳⵓⵏⵜ ⴰⴷ ⵜⵉⴽⵍⵜ ⵉⵣⵡⴰⵔⵏ ⵙⴳ ⵖⵓⵔ “ⴱⵢⵉⵔ ⴷⵉ ⴼⵉⵔⵎⴰ ⴳ 1637 ⴳ ⵜⵙⴳⴰ ⵏ ⵜⵓⵏⵖⵉⵍⵜ “ⴰⵔⵉⵜⵎⵉⵜⵉⴽⴰ” ⵉⵎⴽ ⵉⵏⵏⴰ ⵖⴰⵔⵙ ⴰⵏⵎⵎⴰⵍ ⵉⵎⵖⴰⵔⵏ ⵖⴼ ⴰⴷ ⵉⵜⵜⵓⴳ ⴳ ⵜⵙⴳⴰ.

The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proven in the late 19th century; however, proving that four colors suffice turned out to be significantly harder.

ⵜⵓⵡⵉⴷ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵙⵎⵎⵓⵙ ⵏ ⵉⴽⵯⵍⴰⵏ, ⵖⵓⵔ ⵉⵍⵍⴰ ⵓⵏⵎⵎⴰⵍ ⴰⵎⵣⵡⴰⵔⵓ ⵓⴳⵣⵉⵍ, ⵏ ⵡⵉⵙ ⴳⴰⵏ ⵙⵎⵎⵓⵙ ⵏ ⵉⴽⵯⵍⴰⵏ ⵎⴰⵔ ⴰⴷ ⵜⵜⵓⵖⵎ ⵜⴽⴰⵕⴹⴰ, ⵉⵎⴽ ⵜⵜⵓⴳⴰ ⴳ ⵜⵉⵍⴰⵡⵜ ⴳ ⵜⵢⵉⵔⴰ ⵏ ⵓⵙⴰⵜⵉ ⵡⵉⵙⵙ 19, ⵡⴰⵅⵅⴰ ⵀⴰⴽⴽⴰⴽ, ⵜⵛⵇⵇⴰ ⵜⵉⵏⴰⵡⵜ ⵏ ⵉⵙ ⴳⴰⵏ ⴽⵕⴰⴹ ⵉⴽⵯⵍⴰⵏ.

It was the first major theorem to be proved using a computer.

ⵜⴳⴰ ⵜⴰⵎⴰⴳⵓⵏⵜ ⵜⴰⵅⴰⵜⴰⵔⵜ ⵉⵍⵍⴰⵏ ⴳ ⵜⵉⵏⴰⵡⵜ ⵙ ⵓⵙⵙⵎⵔⵙ ⵏ ⵓⵎⵙⵙⵓⴷⵙ.

Additionally, any map that could potentially be a counterexample must have a portion that looks like one of these 1,936 maps.

ⵜⴰⵔⵏⴰⵡⵜ ⵓⵢⴰ, ⵉⵇⵏⴻⵏ ⴰⴷ ⵢⵉⵍⵉ ⴳ ⴽⵓ ⵜⴰⴽⴰⵕⴹⴰ ⵉⵖⵉⵏ ⴰⴷ ⵉⴳ ⴰⵎⴷⵢⴰ ⴰⵏⵎⴳⴰⵍ, ⵖⴼ ⵜⴳⵣⵣⵓⵎⵜ ⵉⴳⴰⵏ ⵣⵓⵏⴷ ⵜⵉⴽⴰⵕⴹⵉⵡⵉⵏ ⴰⴷ ⵏⵏ ⵉⴳⵓⵍⴰⵏ 1,936 ⵏ ⵜⴽⴰⵕⴹⴰ.

It was originally formulated in 1908, by Steinitz and Tietze.

ⵉⵙⵙⴽⵔⵜ “ⵛⵜⴰⵢⵏⵜⵣ ⴷ ⵜⵉⵜⵣ” ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 1908.

A variety V over a finite field with q elements has a finite number of rational points, as well as points over every finite field with qk elements containing that field.

ⵜⵍⵍⴰ ⴳ ⵡⴰⵏⴰⵡ “ⴼ” ⴳ ⵢⵉⴳⵔ ⵉⵥⵍⵉⵏ ⵙ ⵉⴼⵕⴹⵉⵚⵏ “ⵇ” ⵖⴼ ⵉⵎⵉⴷ ⵉⵥⵍⵉⵏ ⵙⴳ ⵜⵏⵇⵇⴰⴹ ⵜⵓⵎⴳⵉⵏⵉⵏ, ⴷ ⵜⵎⵔⵏⴰⵡⵜ ⵏ ⵜⵏⵇⵇⴰⴹ ⴰⴼⵍⵍⴰ ⵏ ⵢⵉⴳⵔ ⵉⵥⵍⵉⵏ ⴷ ⵉⴼⵕⴹⵉⵚⵏ “ⵇⴽ” ⴳ ⵉⵍⵍⴰ ⵢⵉⴳⵔ ⴰⴷ.

Originally conjectured by Henri Poincaré, the theorem concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold).

ⴳ ⵓⵥⵓⵕ ⵏ ⵜⵡⵏⴳⵉⵎⵜ ⵏ “ⵀⵉⵏⵔⵉ ⴱⵡⴰⵏⴽⴰⵔⵉ” ⵜⴰⵎⴰⴳⵓⵏⵜ ⵢⵓⴳⵍⵏ ⵙ ⵜⴰⵊⵓⵎⵎⴰ ⵉⴳⴰⵏ ⵜⴰⵎⵓⵔⴰⵏⵜ ⵣⵓⵏⴷ ⴰⵙⴰⵢⵔⴰⵔ ⵓⵏⵣⵉⵍ ⵉⵍⴰⵏ ⴽⵕⴰⴹ ⵡⵓⴳⴳⵓⴳⵏ ⵎⴰⴽⴰ ⵎⵎⵙⵍⴰⵖⵏ, ⵉⵍⴰⵏ ⵉⵡⵓⵜⵜⴰ ⴳ ⵓⴽⵙⴰⵢ, ⴷ ⵜⴰⵔ ⵉⵡⵓⵜⵜⴰ ( ⵓⵖⵓⵏ ⵏ 3 ⵡⵓⴳⴳⵓⴳⵏ).

After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv.

ⵣⵓⵏⴷ ⵢⴰⵏ ⵓⵙⴰⵜⵓ ⴰⵢⴰ ⵏ ⵜⵣⵎⵎⴰⵔ ⵏ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵉⵙⵙⵏⴽⴷ “ⴳⵔⵉⴳⵓⵔⵉ ⴱⵉⵔⵉⵍⵎⴰⵏ” ⴰⵏⵎⵎⴰⵍ ⴳ ⴽⵕⴰⴹⵜ ⵜⴼⵔⵜⵉⵏ ⵍⵍⴰⵏⵜ ⴳ 2002 ⴷ 2003 ⴳ “ⴰⵔⵅⴰⵢⴼ” (ⵜⴰⵍⴽⵉⵡⵜ ⵏ ⵜⵎⵃⴹⵉⵜ ⴳ ⴰⵏⵜⵉⵔⵏⵉⵜ).

Perelman completed this portion of the proof.

ⵉⵙⵎⴷ “ⴱⵉⵔⵉⵍⵎⴰⵏ” ⵜⴰⴳⵣⵣⵓⵎⵜ ⴰⴷ ⵏ ⵜⵉⵍⴰⵡⵜ.

Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer; it is widely conjectured that the answer is no.

ⵙ ⵜⵍⵖⴰ ⵓⵔ ⵉⴳⵉⵏ ⵜⵓⵏⵚⵉⴱⵜ, ⴷⴰ ⵉⵙⵇⵙⴰ ⵉⵙ ⵏⵖⵢ ⴰⴷ ⵏⴳ ⵉⴳⵉⵡⵙ ⵏ ⵓⴼⵙⵙⴰⵢ ⵉⵙⵔⴱⵉⵏ ⵉ ⴽⴰ ⵉⴳⴰⵜ ⴷ ⵜⴰⵎⵓⴽⵔⵉⵙⵜ ⵙ ⵓⵎⵙⵙⵓⴷⵙ, ⵉⵎⴽⵉⵏⵏⴰ ⵏⵖⵢ ⴰⴷ ⵜⵜ ⵏⴼⵙⵉ ⴳ ⵓⵎⵙⵙⵓⴷⵙ ⵙ ⵓⵙⵔⴰⵔⵔⵉ, ⴷⴰ ⵉⵜⵢⴰⵖⴰⵍ ⴳ ⵓⴼⵓⵖⴰⵍ ⴰⴱⴰⵔⴰⵡ ⵉⴷ ⵓⵀⵓ.

It has not been proven which one is false, but it is widely believed that the first conjecture is true and the second one is false.

ⴳ ⵜⵉⵍⴰⵡⵜ ⴰⵡⴷ ⵢⴰⵏ ⴷⵉⴽⵙⵏ ⵉⵣⴳⵍⵏ, ⵎⴰⴽⴰ ⴳ ⵜⵍⵍⴰ ⵜⴰⵖⴰⵍⵜ ⴳ ⵓⴼⵓⵖⴰⵍ ⴰⴱⴰⵔⴰⵡ ⵏ ⵡⵉⵙ ⴷ ⴰⵙⵡⵉⵏⴳⵎ ⴰⵎⵣⵡⴰⵔⵓ ⴰⵢⴷ ⵉⴳⵏ ⴰⵎⴷⴷⴰⴷ, ⵡⵉⵙⵙ ⵙⵉⵏ ⵉⵣⴳⵍ.

For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 1012 (over a trillion).

ⵙ ⵓⵎⴷⵢⴰ, ⵜⵜⵓⵙⵜⴰⵢ ⵜⵡⵏⴳⵉⵎⵜ ⵏ “ⴽⵓⵍⴰⵜⵣ” ⵢⵓⴳⵍⵏ ⵙ ⴽⴰⵏ ⵜⴳⴼⴼⵓⵔⵉⵏ ⵏ ⵉⵎⴹⴰⵏ ⵉⵎⴷⴷⴰⴷⵏ; ⴷⴰ ⵜⴼⵓⴽⴽⵓ ⵎⵉⴷ ⵓⵀⵓ, ⵉ ⵓⵎⴰⵜⴰ ⵏ ⵉⵎⴹⴰⵏ ⵉⵎⴷⴷⴰⴷⵏ ⴰⵔ 1.2 × 1012 ( ⵓⴳⴳⴰⵔ ⵏ ⵜⵔⵉⵍⵢⵓⵏ).

That evidence may be of various kinds, such as verification of consequences of it or strong interconnections with known results.

ⵉⵖ ⴰⴷ ⵉⴳ ⵓⵏⵎⵎⴰⵍ ⴰⴷ ⵙⴳ ⵡⴰⵏⴰⵡⵏ ⵉⵎⵣⴰⵔⴰⵢⵏ, ⵣⵓⵏⴷ ⵉⴳⵉⵡⵙ ⴳ ⵜⵍⴽⴰⵎⵉⵏ ⵏⵏⵙ, ⵏⵖⴷ ⵜⴰⵙⵖⵜ ⵉⴷⵓⵙⵏ ⴰⴽⴷ ⵜⵢⴰⴼⵓⵜⵉⵏ ⵉⵜⵜⵢⴰⵙⵙⴰⵏ.

"One method of proof, applicable when there are only a finite number of cases that could lead to counterexamples, is known as ""brute force"": in this approach, all possible cases are considered and shown not to give counterexamples."

“ ⵢⴰⵜ ⴳ ⵜⵖⴰⵔⴰⵙⵉⵏ ⵏ ⵜⵉⵍⴰⵡⵜ ⵉⵍⴰⵏ ⴰⵙⵙⵎⵔⵙ, ⵉⴳ ⵡⴰⵍⵓ ⵖⴰⵙ ⵉⵎⵉⴹ ⴰⵎⵥⵍⴰⵢ ⵡⴰⴷⴷⴰⴷⵏ ⵉⵖⵉⵏ ⴰⴷ ⵢⴰⵡⵢ ⵖⵔ ⵉⵎⴷⵢⴰⵜⵏ ⵉⵏⵎⴳⴰⵍⵏ ⵉⵜⵜⵢⴰⵙⵙⵏ ⵙ “ ⵜⴰⵣⵎⵔⵜ ⵏ ⵓⵎⵓⵜⵜⵍ” ⴳ ⵓⵙⴰⵔⴰ ⴰⴷ, ⴷⴰ ⵉⵜⵜⵉⵍⵉ ⵓⵙⴽⵙⵡ ⵖⵔ ⵡⴰⴷⴷⴰⴷⵏ ⵉⵖⵉⵏ ⴰⴷ ⵢⵉⵍⵉ, ⴷ ⵓⵣⴽⴰⵏ ⵏ ⴰⴷ ⵓⵔ ⵜⵜⵓⴼⴽⵏ ⵉⵎⴷⵢⴰⵜⵏ ⵉⵏⵎⴳⴰⵍⵏ.

The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be independent from the generally accepted set of Zermelo–Fraenkel axioms of set theory.

ⵜⵓⵔⴷⴰ ⵏ ⵓⵣⵣⵉⴳⵣ, ⵏⵏⴰ ⵉⵜⵏⴰⵖⵏ ⴰⴷ ⵜⴳ ⴰⵙⵍⴽⵏ ⵉ ⵜⵣⵍⵖⴰ ⵜⴰⵙⵖⵍⴰⵏⵜ ⵏ ⵉⵜⵙⵏⵜ ⵜⵔⵓⴱⴱⴰ ⵜⴰⵔⵜⵎⵉ, ⴷⴰ ⵜⵙⴱⴰⵢⴰⵏ ⴳ ⵜⵢⵉⵔⴰ ⵎⴰⵙ ⵜⵥⵍⵉ ⵖⴼ ⵜⵔⵓⴱⴱⴰ ⵉⵙⵡⴰⵀⴰⵏ ⵙ ⵓⵎⴰⵜⴰ ⵉ ⵣⵉⵔⵎⵉⵍⵓ-ⴼⵔⵉⵏⴽⵍ, ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵜⵔⵓⴱⴱⴰ.

Few number theorists doubt that the Riemann hypothesis is true.

ⵜⵍⵍⴰ ⵜⵓⵔⴷⴰ ⵏ ⵎⴰⵏⵏⵡ ⵏ ⵉⵎⵙⵙⵉⵥⵉⵔⵏ ⵏ ⵉⵎⴹⴰⵏ ⵖⴼ ⵉⵎⵉⴷⵉ ⵏ ⵜⵓⵔⴷⵓⵜ ⵏ “ⵔⵉⵎⴰⵏ”.

The logistic map is a polynomial mapping, often cited as an archetypal example of how chaotic behaviour can arise from very simple non-linear dynamical equations.

ⵜⴰⴽⴰⵕⴹⴰ ⵜⴰⵍⵉⵊⵉⵙⵜⵉⵜ ⵜⴳⴰ ⵓⵏⵓⵖ ⵏ ⵜⴽⴰⵕⴹⵉⵡⵉⵏ ⵎⵉ ⴳⴳⵓⴷⵉⵏ ⵉⵡⵜⵜⴰ, ⴷⴰ ⵡⴰⵍⴰ ⵜⵓⴱⴷⴰⵔ ⵣⵓⵏⴷ ⴰⵎⴷⵢⴰ ⵏ ⵡⴰⵏⴰⵡ ⵏ ⵎⴰⵎⴽ ⴰⴷ ⵜⵉⵍⵉ ⵜⵉⴽⵍⵉ ⵜⴰⵎⵜⵔⵓⵢⵜ ⵙⴳ ⵜⴳⴷⴰⵣⵓⵍⵉⵏ ⵜⵉⴷⵉⵏⴰⵎⵉⴽⵉⵏ ⵓⵔ ⵉⴳⵉⵏ ⵜⵉⵡⵏⵖⴰⵏⵉⵏ ⵜⵉⵡⵏⵣⴰⵍⵉⵏ ⴽⵉⴳⴰⵏ.

Kepler proved that it is the limit of the ratio of consecutive Fibonacci numbers.

ⵉⵙⵡⵔ “ⴽⵉⴱⵍⵔ” ⵉⴷ ⴰⵡⵜⵜⵓ ⵓⵣⵣⵓⵔ ⵏ ⵓⵙⵖⵍ ⵏ ⵡⵓⵟⵟⵓⵏ “ⴼⵉⴱⵓⵏⴰⵜⵛⵉ” ⵉⵎⵎⵣⴷⴰⵢⵏ.

For two reasons this representation may cause problems.

ⵙ ⵙⵉⵏ ⵉⵙⵔⴰⴳⵏ ⵉⵖⵢ ⵓⵙⵎⴷⵢⴰ ⴰⴷ, ⴰⴷ ⵉⵙⴽⵔ ⵉⵎⵓⴽⵔⵉⵙⵏ.

For example, the two representations 0.999... and 1 are equivalent in the sense that they represent the same number.

ⵙ ⵓⵎⴷⵢⴰ, ⴰⵙⵎⴷⵢⴰ 0.999... ⴷ 1 ⴰⴽⵙⵓⵍⵏ, ⵙⵙⵉⵏ ⴷⴰ ⵙⵙⵏⴽⴰⴷⵏ ⵢⴰⵏ ⵡⵓⵟⵟⵓⵏ.

Using computers and supercomputers, some of the mathematical constants, including π, e, and the square root of 2, have been computed to more than one hundred billion digits.

ⵙ ⵓⵙⵙⵎⵔⵙ ⵏ ⵉⵏⴳⵎⴰⵎⵏ ⵏ ⵓⵎⵙⵙⵓⴷⵙ ⴷ ⵉⵏⴳⵎⴰⵎⵏ ⵏ ⵓⵎⵙⵙⵓⴷⵙ ⵎⵇⵇⵓⵔⵏ, ⵜⵜⵓⵙⵉⵟⵏⵜ ⵜⵔⵙⴰⵍ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴳ ⵢⴰⵎⵓ “π” ⴷ “ⴻ” ⴷ ⵓⵥⵖⵕ ⴰⵎⴽⴽⵓⵥ ⵏ 2 ⵉ ⵏⵏⵉⴳ ⵜⵎⵉⴹⵉ ⵏ ⵉⴼⴹ ⵉⴳⵏⴷⴰⴷ.

Some constants differ so much from the usual kind that a new notation has been invented to represent them reasonably.

ⵎⵣⴰⵔⴰⵢⵏⵜ ⵎⵏⵏⴰⵡ ⵏ ⵉⵎⵣⴳⵉⵜⵏ ⴷ ⵡⴰⵏⴰⵡ ⵉⵍⵍⴰⵏ, ⴰⴳ ⵉⵜⵜⵓⵙⵏⴼⵍⴻⵍ ⵓⵣⵎⵎⴻⵎ ⴰⵎⴰⵢⵏⵓ ⴰⴷ ⵉⵙ ⵉⵙⵎⴷⵢⴰ.

Sometimes, the symbol representing a constant is a whole word.

ⵉⵜⵙⵏⵜ ⵜⵉⴽⴽⴰⵍ, ⵉⵏⵉⴳⵍ ⵉⵙⵙⵏⴽⴰⴷⵏ ⴰⵙⵡⵔ ⵉⴳⴰ ⵜⴰⴳⵓⵔⵉ ⵉⵙⵎⴷⵏ.

0 (zero) is a number, and the numerical digit used to represent that number in numerals.

0 (ⴰⵎⵢⴰ) ⵉⴳⴰ ⵓⵟⵟⵓⵏ, ⴷ ⵡⵓⵟⵟⵓⵏ ⴰⵎⵉⴹⴰⵏ ⴰⴷ ⵉⵜⵜⵓⵙⵎⵔⴰⵙ ⴷ ⴰⵎⵙⵏⴽⴷ ⵏ ⵡⵓⵟⵟⵓⵏ ⵙ ⵡⵓⵟⵟⵓⵏⴻⵏ.

"Names for the number 0 in English include zero, nought (UK), naught (US; ), nil, or—in contexts where at least one adjacent digit distinguishes it from the letter ""O""—oh or o."

ⵉⵍⵍⴰ ⴳ ⵢⵉⵙⵎⴰⵡⵏ ⵏ 0 ⴳ ⵜⵏⴳⵍⵉⵣⵜ “ⴰⵎⵢⴰ”, ⵏⵖⴷ ⴰⵡⵡⴷ (ⵜⴰⴳⵍⴷⵉⵜ ⵉⵎⵓⵏⵏ), ⵏⵖⴷ ⴰⵡⴷⵃⴰⵃ (ⵜⵉⵎⵥⵍⴰⵢ ⵓⵎⵓⵏⵏ), ⵏⵖⴷ ⴰⵡⵡⴷ ⴳ ⵉⵙⴰⵜⴰⵍⵏ ⴳ ⵏⵙⵏⵓⵃⵢⵓ ⵓⵟⵟⵓⵏ ⵢⴰⵏ ⴷ ⵓⵙⴽⴽⵉⵍ “ⵓ” (ⵎⵇⵇⵓⵔⵏ) ⵏⵖⴷ “ⵓ” (ⵎⵥⵥⵉⵢⵏ).

For the simple notion of lacking, the words nothing and none are often used.

ⵉ ⵓⵔⵎⵎⵓⵙ ⴰⵅⵚⵚⴰ ⵓⵏⵣⵉⵍ ⴷⴰ ⵡⵍⴰ ⵜⵜⵓⵙⵙⵎⵔⴰⵙⵏⵜ ⵜⴳⵓⵔⵉⵡⵉⵏ ⴰⵎⵢⴰ ⴷ ⴰⵡⵜⵃⴰⵃ.

It is often called oh in the context of telephone numbers.

ⴷⴰ ⴰⵙ ⵜⵜⵉⵏⵉⵏ “ⵓⵀ” ⴳ ⵓⵙⴰⵜⴰⵍ ⵏ ⵡⵓⵟⵟⵓⵏ ⵏ ⵜⵉⵍⵉⴼⵓⵏ.

The symbol nfr, meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids, and distances were measured relative to the base line as being above or below this line.

ⵉⵎⴽⵉⵏⵏⴰ ⵜⵜⵓⵙⵎⵔⵙ ⵜⵎⴰⵜⴰⵔⵜ “ⵏⴼⵔ”, ⵉⴳⴰⵏ ⴰⴼⵓⵍⴽⵉ, ⵎⴰⵔ ⴰⴷ ⵉⵜⵜⵓⵏⵄⵜ ⵓⵙⵡⵉⵔ ⴰⵙⵉⵍⴰⵏ ⴳ ⵡⵓⵏⵓⵖⵏ ⵏ ⵉⵙⵎⴹⴰⵍ ⴷ ⵉⵣⴰⵎⵓⴳⵏ, ⵉⵎⴽ ⵜⵜⵓⵙⵖⴰⵍ ⵓⵙⵜⵓⵎ ⵏ ⵉⵣⵔⵉⵔⵉⴳ ⴰⵙⵉⵍⴰ ⵉⵜⵜⵉⵍⵉⵏ ⴰⴼⵍⵍⴰ ⵏⵖⴷ ⴷⴷⴰⵡ ⵓⵣⵔⵉⵔⵉⴳ ⴰⴷ.

The Babylonian placeholder was not a true zero because it was not used alone, nor was it used at the end of a number.

ⵓⵔ ⵉⴳⵉ ⵓⴼⵕⴹⵉⵚ ⴰⴹⴼⴰⵕ ⵏ ⴱⴰⴱⵉⵍⵉ ⴰⵎⵢⴰ ⵉⵎⵉⴷⵉ, ⴰⵛⴽⵓ ⵓⵔ ⵉⵜⵜⵓⵙⵙⵎⵔⴰⵙ ⵉ ⵡⴰⴹⵓ ⵏⵏⵙ, ⴷ ⵓⵔ ⵉⵜⵜⵓⵙⵎⵔⴰⵙ ⴳ ⵜⵢⵉⵔⴰ ⵏ ⵡⵓⵟⵟⵓⵏ.

By AD 150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest.

ⴰⴷⴷⴰⵢ ⵜⴰⵡⴹ 150 ⴹⴰⵕⵜ ⵜⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ, ⵉⵙⵏⵏⴷ “ⴱⴰⵟⵍⵉⵎⵓⵙ” ⵖⵔ “ⴱⵀⵉⴱⴰⵔⵅⵓⵙ” ⴷ “ⴱⴰⴱⵉⵍⵢⵢⵉⵏ” ⴷⴰ ⵉⵙⵙⵎⵔⴰⵙ ⵜⴰⵏⴳⴰⵍⵜ ⵉ ⵓⵎⵢⴰ ⴳ ⵜⵡⵓⵔⵉ ⵏ ⵜⵓⵙⵏⵉⵜⵔⴰⵏ ⵜⴰⵡⵙⵏⴰⴽⵜ ⵎⵉ ⵜⵜⵉⵏⵉⵏ “ⵜⴰⵊⵕⵕⵓⵎⵜ ⵜⴰⵡⵙⵏⴰⴽⵜ”, ⵜⵢⴰⵙⵙⵏ ⴰⵡⴷ ⵙ “ⴰⵍⵎⴰⵊⵉⵙⵜ”.

"This use was repeated in AD525 in an equivalent table, that was translated via the Latin nulla or ""none"" by Dionysius Exiguus, alongside Roman numerals."

“ⵉⵜⵜⵓⵢⴰⵍⵙ ⵓⵙⵙⵎⵔⵙ ⴰⴷ ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 525 ⴹⴰⵕⵜ ⵜⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ ⴳ ⵓⵙⵎⵢⴰⵍⵍⴰⵢ ⵏ ⵓⵙⵙⵉⴽⵙⵍ, ⵉⵙⵙⵓⵖⵍⵜ ⵙ “ⵓⵎⵢⴰ” ⴷⵢⵓⵏⵉⵙⵢⵓⵙ ⵉⴽⵙⵉⵊⵓⵙ ⵙⴳ ⵜⵍⴰⵜⵉⵏⵉⵜ, ⵉⵎⴽ ⵉⵎⵎⵙⵍⴰⵖ ⴷ ⵡⵓⵟⵟⵓⵏ ⵉⵕⵓⵎⴰⵏⵉⵜⵏ”.

The Lokavibhāga, a Jain text on cosmology surviving in a medieval Sanskrit translation of the Prakrit original, which is internally dated to AD 458 (Saka era 380), uses a decimal place-value system, including a zero.

“ⵍⵓⴽⴰⴼⵉⴱⴰⴳⴰ” ⵉⴳⴰⵏ ⴰⴹⵕⵉⵚ ⵏ “ⵊⴰⵢⵏ” ⵉⵙⴰⵡⴰⵍⵏ ⵖⴼ ⵜⵓⵙⵏⴰⵖⵣⵡⵔⵜ ⵉⵙⵓⵍⵏ ⵉⴷⴷⵔ ⴳ ⵓⵙⵓⵖⵍ ⵏ “ⵙⴰⵏⵙⴽⵔⵉ” ⵉⴳⴰⵏ ⵡⵉⵏ “ⴱⵔⴰⴽⵔⵉ”, ⵙⴳ ⵉⵣⵎⴰⵣⵏ ⵉⵏⴰⵎⵎⴰⵙⵏ, ⵏⵏⴰ ⵉⵍⵍⴰⵏ ⴳ ⵓⵙⴰⴽⵓⴷ 458 ⴹⴰⵕⵜ ⵜⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ ( ⴰⵣⵎⵣ ⵏ ⵙⴰⴽⴰ 380), ⵉⵙⵙⵎⵔⴰⵙⵏ ⴰⵏⴳⵔⴰⵡ ⵏ “ⵡⴰⵜⵉⴳ ⴰⴷⵖⴰⵔⴰⵏ ⴰⵎⵔⴰⵡ” ⴳ ⵢⴰⵎⵓ ⵓⵎⵢⴰ.

"In 813, al-Khwarizmi used the Hindu numerals in his astronomical tables."""

“ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 813, ⵉⵙⵙⵎⵔⵙ “ⴰⵍⵅⴰⵡⴰⵔⵉⵣⵎ” ⵓⵟⵟⵓⵏ ⵉⵀⵉⵏⴷⵉⵢⵏ ⴳ ⵉⵙⵎⵢⴰⵍⵍⴰⵢⵏ ⵏⵏⵙ ⵉⵡⵜⵔⴰⵏⴻⵏ.”

This book was later translated into Latin in the 12th century under the title Algoritmi de numero Indorum.

ⵉⵜⵜⵓⵙⵓⵖⵍ ⵓⴷⵍⵉⵙ ⴰⴷ ⵖⵔ ⵜⵍⴰⵜⵉⵏⵉⵜ ⴳ ⵓⵙⴰⵜⵓ ⵡⵉⵙⵙ 12 ⴷⴷⴰⵡ ⵓⵣⵡⵍ “ⴰⵍⴳⵓⵔⵉⵜⵎ ⵏ ⵡⵓⵟⵟⵓⵏ ⵉⵏⴷⵓⵔⵓⵎ”.

I pursued my study in depth and learned the give-and-take of disputation.

ⵙⵎⴷⵖ ⵜⴰⵖⵓⵔⵉ ⵉⵏⵡ ⵙ ⵜⵉⴷⵔⵓⵜ, ⴷ ⵍⵎⴷⵖ ⵜⵉⴽⴽⵉ ⴷ ⵢⵉⵎⵥ ⴳ ⵓⵎⵣⵉⵔⴰⵢ.

I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.

ⴳⵉⵖ ⵜⵉⵣⵎⵎⴰⵔ ⵎⴰⵔ ⴰⴷ ⵙⵙⵓⴼⵖ ⴰⴷⵍⵉⵙ ⴰⴷ ⴽⵓⵍⵍⵓⵜ ⵙ ⵓⵢⵏⵏⴰ ⵎⵉ ⵣⴹⴰⵕⵖ, ⴷ ⴱⴹⵉⵖⵜ ⵖⴼ ⵙⵎⵎⵓⵙ ⴷ ⵎⵔⴰⵡ ⵏ ⵜⵙⴷⴷⴰⵔⵜ.

The nine Indian figures are: 9 8 7 6 5 4 3 2 1.

ⵜⵥⴰ ⵏ ⵡⵓⵟⵟⵓⵏ ⵉⵀⵉⴷⵉⵜⵏ: 9 8 7 6 5 4 3 2 1.

254–255 include 0 as a natural number, in which case it is the only natural number that is not positive.

254-255 ⵜⵙⵎⴰⵏ 0 ⵓⵟⵟⵓⵏ ⴰⵖⴰⵔⴰⵏ, ⴳ ⵡⴰⴷⴷⴰⴷ ⴰⴷ ⴷⴰ ⵉⵜⴳⴳⴰ ⵡⵓⵟⵟⵓⵏ ⴰⵖⴰⵔⴰⵏ ⵉ ⵡⴰⴹⵓⵏ ⵏⵏⵙ ⵓⵔ ⵉⴳⵉⵏ ⵓⵎⵏⵉⴳ.

As a value or a number, zero is not the same as the digit zero, used in numeral systems with positional notation.

ⴰⵜⵉⴳ ⵏⵖⴷ ⵓⵟⵟⵓⵏ, “ⴰⵎⵢⴰ” ⵓⵔ ⵉⴷ ⵏⵜⵜⴰ ⵏⵏⵉⴽ ⴰⵢⴷ ⵉⴳⴰⵏ “ⴰⵡⵜⵃⴰⵃ”, ⵉⵜⵜⵓⵙⵎⵔⴰⵙⵏ ⴳ ⵉⴳⵔⵔⴰⵢⵏ ⵉⵎⴰⵟⵟⵓⵏⴻⵏ ⵉⵍⴰⵏ ⵜⴰⵎⴰⵜⴰⵔⵜ ⵏ ⵓⵙⵓⵔⵙ.

The number 0 may or may not be considered a natural number, but it is an integer, and hence a rational number and a real number (as well as an algebraic number and a complex number).

ⵓⵟⵟⵓⵏ 0 ⵉⵜⵜⵓⵙⵏⴼⵍ ⵏⵖⴷ ⵓⵔ ⵉⴳⵉ ⵉⵎⵉⴹ ⴰⵖⴰⵔⴰⵏ, ⵎⴰⴽⴰ ⵉⵎⵉⴹ ⴰⵎⴷⴷⴰⴷ ⵉⴳⵏ ⵓⵟⵟⵓⵏ ⵓⵎⴳⵉⵏ ⴷ ⴰⵖⴰⵔⴰⵏ (ⴷ ⵜⵔⵏⵓⵜ ⵏ ⵡⵓⵟⵟⵓⵏ ⴰⵊⵉⴱⵔⵉ ⴷ ⵡⵓⵟⵟⵓⵏ ⵓⴷⴷⵉⵙ).

It cannot be prime because it has an infinite number of factors, and cannot be composite because it cannot be expressed as a product of prime numbers (as 0 must always be one of the factors).

ⵓⵔ ⵉⵖⵉⵢ ⴰⴷ ⵉⴳ ⵉⵎⵉⴹ ⴰⵎⵣⵡⴰⵔⵓ ⴰⵛⴽⵓ ⴷⵉⴽⵙ ⴽⵉⴳⴰⵏ ⵏ ⵡⴰⵎⵎⴰⴽⵏ, ⴷ ⵉⵣⴹⴰⵕ ⴰⴷ ⵉⴳ ⵓⴷⴷⵉⵙ ⴰⵛⴽⵓ ⵏⵖⵉⵢ ⴰⴷ ⵖⵉⴼⵙ ⵏⵙⵉⵡⵍ ⴷ ⴰⴼⴰⵔⵙ ⵏ ⵉⵎⴹⴰⵏ ⵉⵎⵣⵡⵓⵔⴰ ( ⵉⵎⴽ ⵏⵏ ⵉⵇⵏⴻⵏ ⴰⴷ ⴰⵀⴰ ⵉⴳ 0 ⵢⴰⵏ ⴳ ⵡⴰⵎⵎⴰⴽⵏ).

These rules apply for any real or complex number x, unless otherwise stated.

ⴷⴰ ⵜⵜⵓⴳⴰⵏ ⵉⵍⴳⴰⵎⵏ ⴰⴷ ⵖⴼ ⴽⴰ ⵉⴳⴰⵜ ⵓⵟⵟⵓⵏ ⴰⵖⴰⵔⴰⵏ ⵏⵖⴷ ⵓⴷⴷⵉⵙ “ⴽ” ⵉⴳ ⵓⵔ ⵉⴳⵉ ⴰⴽⵏⴰⵙ ⵏ ⵎⴰⵢⴰⵏ.

The cardinality function, applied to the empty set, returns the empty set as a value, thereby assigning it 0 elements.

ⴷⴰ ⵜⵜⵓⵖⵓⵍ ⵜⵏⴰⵎⴽⴰⵏⵜ ⵏ ⵓⵣⴷⴷⵓⵢ ⴰⴷⵙⵍⴰⵏ ⵉⵜⵜⵓⵙⵎⵔⴰⵙⵏ ⵖⴼ ⵜⵔⴰⴱⴱⵓⵜ ⵉⵅⵡⴰⵏ, ⵜⴰⵔⴰⴱⴱⵓⵜ ⵉⵅⵡⴰⵏ ⵉⴳⵏ ⴰⵜⵉⴳ, ⵜⴳ ⵜⵉⵙⵙⵉⴼⵜ ⵏⵏⵙ 0 ⵏ ⵉⴼⵕⴹⵉⵚⵏ.

In abstract algebra, 0 is commonly used to denote a zero element, which is a neutral element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined).

ⴳ ⵍⵊⵉⴱⵔ ⴰⵡⵏⴳⵉⵎ, ⴷⴰ ⵡⴰⵍⴰ ⵉⵜⵜⵓⵙⵎⵔⴰⵙ 0 ⴰⴷ ⵉⴳ ⵜⴰⵏⵄⵜ ⵏ ⵓⴼⵕⴹⵉⵚ ⴰⵎⵢⴰ; ⴷ ⵏⵜⵜⴰ ⴰⴼⵕⴹⵉⵚ ⴰⵔⴰⵡⵙⴰⵏ ⵏ ⵜⵎⵔⵏⵉⵡⵜ (ⵉⴳ ⵉⵜⵜⵢⴰⴽⵣ ⴳ ⵜⵓⵙⴽⵉⵡⵜ ⵜⴰⵎⵣⵔⴰⵡⵜ), ⴷ ⵓⴼⵕⴹⵉⵚ ⵉⵙⵙⵓⵎⵓⵎⵏ ⴰⵙⴼⵓⴽⵜⵉ (ⵉⴳ ⵉⵜⵜⵢⴰⴽⵣ).

For some quantities, the zero level is naturally distinguished from all other levels, whereas for others it is more or less arbitrarily chosen.

ⴳ ⵉⵜⵙⵏ ⵉⵡⵓⴷⵉⵢⵏ, ⴷⴰ ⵉⵜⵜⵓⵙⵏⵓⵃⵢⵓ ⵓⵙⵡⵉⵔ ⵏ ⵓⵎⵢⴰ ⵙ ⵜⴰⵍⵖⴰ ⵜⴰⵖⴰⵔⴰⵏⵜ ⴷ ⵉⵙⵡⵉⵔⵏ ⵏⵏⵉⴹⵏ, ⴰⵔ ⵉⵜⵜⵓⵙⵜⴰⵢ ⵙ ⵜⴰⵍⵖⴰ ⵜⴰⵙⵇⴷⴷⵛⵜ ⵙ ⵓⵡⵜⵜⵓ ⴰⴽⴷ ⵉⵜⵙⵏ ⵢⴰⴹⵏ.

It has been shown that a cluster of four neutrons may be stable enough to be considered an atom in its own right.

ⵜⴰⵔⴰⴱⴱⵓⵜ ⵜⴰⵎⴽⴽⵓⵥⵜ ⵏ ⵏⵉⵜⵔⵓⵏ ⵜⵜⵓⵡⵔ ⵉⵙ ⵜⵖⵢ ⴰⴷ ⵜⵣⵣⴳⴰ ⴰⵔ ⵢⴰⵜ ⵜⵙⴽⵯⴼⵍⵜ ⵉⴼⵓⴽⵏ, ⵉⵎⴽ ⵉⵖⵢ ⴰⴷ ⵜⴳ ⵏⵜⵜⴰⵜ ⵏⵏⵉⴽ ⵜⴰⴱⵍⴽⵎⵜ.

For example, the elements of an array are numbered starting from 0 in C, so that for an array of n items the sequence of array indices runs from 0 to .

ⵙ ⵓⵎⴷⵢⴰ, ⴷⴰ ⵜⵜⵓⵙⵏⵇⴹⵏ ⵉⴼⵕⴹⵉⵚⵏ ⵏ ⵜⴰⴷⵓⵔⵜ ⵙⴳ “0” ⴳ “ⵙ”, ⴰⵔ ⵜⵜⵓⵙⵡⵓⵔⵉ ⵜⵙⵏⵙⵍⵜ ⵏ ⵜⵙⴽⵜⵓⵔⵉⵏ ⵏ ⵜⴰⴷⵓⵔⵜ ⵙⴳ 0 ⴰⵔ .

In databases, it is possible for a field not to have a value.

ⴳ ⵉⵍⴳⴰⵎⵏ ⵏ ⵉⵙⴼⵔⵓⵜⵏ, ⵉⵖ ⴰⴷ ⵓⵔ ⵢⵉⵍⵉ ⵢⵉⴳⵔ ⴰⵜⵉⴳ.

For text fields this is not blank nor the empty string.

ⴳ ⵢⵉⴳⵔⴰⵏ ⵓⴹⵕⵉⵚⵏ, ⵡⴰⴷ ⵓⵔ ⵉⵅⵡⵉ ⵓⵍⴰ ⵉⴳⴰ ⵜⴰⴳⴼⴼⵓⵔⵜ ⵏ ⵉⵅⵡⴰⵏ.

Any computation including a null value delivers a null result.

ⴽⴰ ⵉⴳⴰⵜ ⴰⵙⵙⵉⵟⵏ ⴷⵉⴽⵙ ⴰⵜⵉⴳ ⵉⵅⵡⴰⵏ ⵉⵜⵜⴰⵎⵥⵏ ⵜⴰⵢⴰⴼⵓⵜ ⵉⵅⵡⴰⵏ.

In Formula One, if the reigning World Champion no longer competes in Formula One in the year following their victory in the title race, 0 is given to one of the drivers of the team that the reigning champion won the title with.

ⴳ “ⵍⴼⵓⵔⵎⵓⵍⴰ ⵡⴰⵏ” ⵉⴳ ⵓⵔ ⴷⴰ ⵉⵜⵜⵎⵣⵉⵣⵡⵔ ⵓⵏⴱⵔⴰⵣ ⴰⵎⴰⴹⵍⴰⵏ ⴳ “ⵍⴼⵓⵔⵎⴰⵍⴰ ⵡⴰⵏ” ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⴳ ⵓⵡⵉⵏ ⵜⴰⵙⵎⵖⵓⵔⵜ, ⴷⴰ ⵉⵜⵜⵓⴼⴽⴰ 0 ⵉ ⵢⴰⵏ ⴳ ⵉⵎⵃⵔⴰⵢ ⵏ ⵜⵔⴰⴱⴱⵓⵜ ⵢⵓⵡⵉⵏ ⵜⴰⵙⵎⵖⵔⵜ.

Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0.

ⵓⵔ ⴷⴰ ⵙⵎⵣⵉⵔⵉⵢⵏ ⵉⵎⴰⵙⵙⵏ ⵏ ⵜⴰⵔⴰⵢⵜ ⴳⵔ “O” ⴷ “0” ⵎⵏⵏⴰⵡ ⵏ ⵡⴰⵣⵓⵔⵜ ⵓⵔ ⵖⴰⵔⵙ ⵜⴰⵙⴰⵔⵓⵜ ⵏ ⵓⵙⵎⵣⵉⵔⴰⵢ ⵏ ⵡⵓⵟⵟⵓⵏ 0.

The digit 0 with a dot in the center seems to have originated as an option on IBM 3270 displays and has continued with some modern computer typefaces such as Andalé Mono, and in some airline reservation systems.

ⵉⴳⴰ ⵡⵓⵟⵟⵓⵏ 0 ⵉⵍⴰⵏ ⵜⴰⵏⵇⵇⵉⴹⵜ ⴳ ⵡⴰⵎⵎⴰⵙ ⵉⵜⵜⵓⵙⴽⴰⵔ ⴷ ⴰⴷⴰⵖⴰⵔ ⴳ ⵉⵎⵉⵥⴰⵕⵏ “ⵉⴱⵎ 3270”, ⵉⵙⵙⵓⴷⴰ ⴰⴽⴷ ⴽⴰⵏ ⵜⴰⵔⴰⵢⵉⵏ ⵏ ⵓⵎⵙⵙⵓⴷⵙ ⴰⵎⴰⵢⵏⵓ ⵣⵓⵏⴷ ⴰⵏⴷⴰⵍⵉ ⵎⵓⵏⵓ, ⴷ ⵛⴰ ⵏ ⵉⴳⵔⵔⴰⵢⵏ ⵏ ⵡⵓⴹⵓⴼ ⵏ ⵜⴷⵔⴰⵡⵉⵏ ⵏ ⵡⴰⵢⵍⴰⵍ.

1 (one, also called unit, and unity) is a number and a numerical digit used to represent that number in numerals.

1 (ⵢⴰⵏ, ⵉⴳⴰ ⴰⵡⴷ ⵜⴰⴼⵔⴷⵉⵙⵜ, ⵜⴰⴳⵣⵣⵓⵎⵜ) ⵉⴳⴰⵏ ⵓⵟⵟⵓⵏ ⴷ ⴰⵎⵟⵟⵓⵏ ⴷⴰ ⵉⵜⵜⵓⵙⵎⵔⴰⵙ ⴳ ⵓⵙⵎⴷⵢⴰ ⵏ ⵡⵓⵟⵟⵓⵏ ⴳ ⵓⵎⵟⵟⵓⵏ.

In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer.

ⴳ ⵉⵔⵎⴰⵏ ⵏ ⵜⵎⵓⵍⵉ ⴳ ⵓⵔ ⵉⴳⵉ ⵓⵎⵢⴰ ⵓⵎⵏⵉⴳ ⵡⴰⵍⴰ ⵓⵣⴷⵉⵔ, 1 ⴰⵢⴷ ⵉⴳⴰⵏ ⵉⵎⵉⴹ ⴰⵎⵣⵡⴰⵔⵓ ⴷ ⴰⵎⵥⵥⴰ ⴷ ⴰⵎⴷⴷⴰⴷ ⵓⵎⵏⵉⴳ.

Most if not all properties of 1 can be deduced from this.

ⵉⵖⵜ ⴰⴷ ⵙⴼⵍⵓ ⴽⵉⴳⴰⵏ ⴳ ⵉⵎⵥⵍⴰⵢ ⵏ 1, ⵎⴽ ⴰⴽⴽⵯ ⵓⵔ ⴳⵉⵏ ⵙⴳ ⵓⵢⴰ .

It is thus the integer after zero.

ⴷ ⵏⵜⵜⴰ ⵉⵎⵉⴹ ⴰⵎⴷⴷⴰⴷ ⴹⴰⵕⵜ ⵓⵎⵢⴰ.

It was transmitted to Europe via the Maghreb and Andalusia during the Middle Ages, through scholarly works written in Arabic.

ⵉⵜⵜⵓⵙⵎⵓⵜⵜⵢ ⵖⵔ ⵓⵔⵓⴱⴱⴰ ⵙⴳ ⵍⵎⵔⵔⵓⴽ ⴷ ⵍⴰⵏⴷⴰⵍⵓⵙ ⴳ ⵉⵣⵎⴰⵣ ⵉⵏⴰⵎⵎⴰⵙⵏ, ⵙ ⵜⵡⵓⵔⵉⵡⵉⵏ ⵜⵉⵎⴰⵙⵙⴰⵏⵉ ⵉⵜⵢⴰⵔⴰⵏ ⵙ ⵜⵄⵔⴰⴱⵜ.

Styles that do not use the long upstroke on digit 1 usually do not use the horizontal stroke through the vertical of the digit 7 either.

ⵉⵎⴰⵎⴽⵏ ⵓⵔ ⵉⵜⵜⵓⵙⵎⵔⴰⵙⵏ ⴳ ⵜⴰⴷⵓⵣⵜ ⵜⴰⵖⵣⵣⴰⴼⵜ ⵖⴼ ⵡⵓⵟⵟⵓⵏ 1, ⵓⵔ ⴷⴰ ⵡⴰⵍⴰ ⵜⵙⵙⵎⵔⴰⵙ ⴰⴼⵙⵜ ⴰⵏⵍⵍⵉ ⵜⴰⵎⴰⴼⵍⵍⴰⵜ ⴳ ⵜⵔⵙⵍⵜ ⵜⴰⵡⴼⵍⵍⴰⵜ ⵏ ⴰⵡⴷ ⵡⵓⵟⵟⵓⵏ 7.

By definition, 1 is the magnitude, absolute value, or norm of a unit complex number, unit vector, and a unit matrix (more usually called an identity matrix).

ⵙⴳ ⵓⵙⵏⵎⵍ, 1 ⵉⴳⴰ ⴰⴽⵙⴰⵢ ⵏⵖⴷ ⴰⵜⵉⴳ ⵉⴼⵓⴽⵏ ⵏⵖⴷ ⴰⵏⴰⵡⴰⵢ ⵉ ⵜⴳⵣⵣⵓⵎⵜ ⵏ ⵉⵎⵉⴹ ⵓⴷⴷⵉⵙ, ⴷ ⵓⵎⵏⵉⴷ ⵏ ⵜⴳⵣⵣⵓⵎⵜ ⴷ ⵜⴰⴷⵓⵔⵜ ⵏ ⵜⴳⵣⵣⵓⵎⵜ (ⵉⵜⵢⴰⵙⵙⵏ ⵙ: ⵜⴰⴷⵓⵔⵜ ⵏ ⵜⵎⴰⴳⵉⵜ).

In category theory, 1 is sometimes used to denote the terminal object of a category.

ⴳ ⵜⵎⴰⴳⵓⵏⵜⵏ ⵜⴳⵔⵔⵓⵎⴰ, ⴷⴰ ⵉⵜⵜⵓⵙⵎⵔⴰⵙ 1 ⵉⵜⵙⵏⵜ ⵜⵉⴽⴽⴰⵍ ⵎⴰⵔ ⴰⴷ ⵉⵜⵜⵓⵏⵄⵜ ⵓⵎⵙⵖⴰⵔⵓ ⴰⵎⴳⴳⴰⵔⵓ ⵏ ⵜⴳⵔⵔⵓⵎⴰ.