Can the absolute value be negative?

No, by definition, the absolute value is always zero or positive.

What is the absolute value of zero?

The absolute value of zero is zero.

Is 'modulus' always a synonym for 'absolute value'?

In real numbers, yes. For complex numbers, 'modulus' refers to the analogous concept (distance from the origin in the complex plane).

Why is absolute value important?

It simplifies problems involving magnitude or distance, and is essential in solving equations, inequalities, and modeling real-world scenarios where only size matters, not direction.

absolute value

UK/ˌæbsəluːt ˈvæljuː/US/ˈæbsəˌlut ˈvælju/

Technical (Mathematics), Academic

My Flashcards

Definition

Meaning

The non-negative magnitude of a real number, disregarding its sign; symbolized as |x|.

A measure of magnitude or distance from zero, used in mathematics and physics; figuratively, an unwavering principle or standard.

Linguistics

Semantic Notes

In mathematics, it is a unary operation. Its figurative use ('moral absolute values') is less common but understood.

Dialectal Variation

British vs American Usage

Differences

No significant lexical or usage differences; a technical term identical in both variants.

Connotations

Neutral, purely mathematical/technical in both.

Frequency

Equally frequent in academic/technical contexts in both regions.

Vocabulary

Collocations

strong

calculate thefind themodulusfunctionof a number

medium

thepositivemagnitudedistance from zero

weak

greatsmallnumerical

Grammar

Valency Patterns

the absolute value of [NUMBER]compute |x|

Vocabulary

Synonyms

Strong

modulus (complex numbers)

Neutral

magnitudemodulus

Weak

sizedistance from zero

Vocabulary

Antonyms

signed value

Usage

Context Usage

Business

Rare, except in data analysis (e.g., 'absolute value of the error').

Academic

Core concept in algebra, calculus, and complex analysis.

Everyday

Virtually never used in casual conversation.

Technical

Fundamental term in mathematics, physics, engineering, and programming.

Examples

By Part of Speech

adjective

British English

The absolute-value function is continuous.

American English

Graph the absolute-value expression.

Examples

By CEFR Level

The absolute value of 5 is 5.
The absolute value of -3 is 3.

To find the absolute value, ignore the minus sign.
On a number line, the absolute value is the distance to zero.

You must consider the absolute value when solving this equation.
The program calculates the absolute value of each input.

The properties of the absolute value function are foundational in analysis.
Inequalities involving absolute values require case analysis.

Learning

Memory Aids

Mnemonic

Think of a number's distance from zero on a number line; the sign (+ or -) is ignored, so the distance is always positive or zero.

Conceptual Metaphor

DISTANCE FROM ZERO (Mathematical); UNWAVERING STANDARD (Figurative).

Watch out

Common Pitfalls

Translation Traps (for Russian speakers)

Do not translate word-for-word as 'абсолютная ценность' (which means 'absolute worth'). The correct equivalent is 'абсолютная величина' or 'модуль'.
The concept is identical in mathematics, but the lexical item is fixed.

Common Mistakes

Using 'absolute value' to mean 'exact value' or 'complete value' in non-mathematical contexts.
Forgetting it is non-negative; e.g., saying 'the absolute value is -5'.
Confusing the notation |x| with parentheses or brackets.

Practice

Quiz

Fill in the gap

The of -7 is 7.

Multiple Choice

Which of these best defines 'absolute value'?

FAQ

Frequently Asked Questions

: No, by definition, the absolute value is always zero or positive.
: The absolute value of zero is zero.
: In real numbers, yes. For complex numbers, 'modulus' refers to the analogous concept (distance from the origin in the complex plane).
: It simplifies problems involving magnitude or distance, and is essential in solving equations, inequalities, and modeling real-world scenarios where only size matters, not direction.