Nonnegative means greater than or equal to zero: such a number is either 0 or positive, so x ≥ 0. The nonnegative integers are 0, 1, 2, 3 and so on. It is not the same as positive, because 0 is nonnegative but not positive. Distances, absolute values and principal square roots are always nonnegative.
In Spanish
no negativo
Also called
non-negative, not negative, greater than or equal to zero, zero or positive
Grade level
6-8
Grade 6Grade 7Algebra 1SATACTGEDACCUPLACERHiSET
Nonnegative in a picture
Nonnegative and positive shade the same region; the difference is the dot at 0. Nonnegative includes 0, positive does not.
Formal definition and notation
A real numberx is nonnegative if x ≥ 0, that is, if x > 0 or x = 0. The set of nonnegative real numbers is the interval [0, ∞), and the nonnegative integers are {0, 1, 2, 3, …}, the whole numbers. Similarly, nonpositive means x ≤ 0.
Symbol
Read it as
Meaning
x ≥ 0
x is greater than or equal to zero
x is nonnegative
[0, ∞)
the interval from zero to infinity, including zero
all nonnegative real numbers
Key facts
Nonnegative = ≥ 0. Positive = > 0. The only number that is nonnegative but not positive is 0.
Nonnegative numbers can be fractions or decimals: 0.5 and 73 are nonnegative.
Tests use the word to rule out negative answers: if x is nonnegative and x2 = 25, then x = 5 only.
For √x to be a real number, the expression under the root must be nonnegative.
Try it: x ≥ 0
Interactive
The ray shows every nonnegative number, x ≥ 0. Use the left-end button to switch the dot at 0 from closed to open: that changes nonnegative into positive.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Nonnegative examples, step by step
Example 1: Sort the numbers
Warm-up
Which of these are nonnegative: −3, 0, 2.5, −0.1, 7?
Nonnegative means ≥ 0.
−3 and −0.1 are below 0, so they are out.
0 is equal to 0, so it is in; 2.5 and 7 are above 0.
Answer: The nonnegative numbers are 0, 2.5 and 7.
Example 2: When is a square root real?
Core
For which values of x is √x − 4 a real number?
The expression under the root must be nonnegative: x − 4 ≥ 0.
The whole numbers 0, 1, 2, 3 and so on are exactly the nonnegative integers. Nonnegative alone also allows fractions such as 2.5.
Quick check: 3 questions
Question 1 of 3
Which number is nonnegative but NOT positive?
Show answer and explanation
Answer: D. 0 is greater than or equal to 0, so it is nonnegative, but it is not greater than 0, so it is not positive. 1 and 0.01 are both, and −1 is neither.
Question 2 of 3
x is nonnegative and |x − 2| = 5. What is x?
Show answer and explanation
Answer: B.x − 2 = 5 or x − 2 = −5, so x = 7 or x = −3. Only 7 is nonnegative. D ignores the condition, and 3 is a sign error.
Question 3 of 3
How many nonnegative integers are less than 6?
Show answer and explanation
Answer: A. 0, 1, 2, 3, 4, 5: six numbers. 5 forgets 0, 7 wrongly includes 6, and 4 drops both ends.
Nonnegative: frequently asked questions
Is zero nonnegative?
Yes. Nonnegative means greater than or equal to zero, and zero is equal to zero, so it qualifies. Zero is not positive and not negative, which is exactly why test writers use the word nonnegative: it signals that 0 is an allowed value, for example in nonnegative integers 0, 1, 2 and so on.
What is the difference between positive and nonnegative?
Positive numbers are greater than 0, written x > 0. Nonnegative numbers are greater than or equal to 0, written x ≥ 0. The two sets are identical except for the number 0, which is nonnegative but not positive. On a number line, positive uses an open dot at 0 and nonnegative a closed dot.
Are nonnegative numbers always integers?
No. Nonnegative only describes the sign. 0.75, 94 and π are all nonnegative. When a problem wants whole numbers too, it says nonnegative integer, which means one of 0, 1, 2, 3 and so on. Read both words of the phrase before you list values.
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