CONCEPTS OF ZERO
Zero is a special and unusual number. As you read above, it has an interesting history. What do you know about zero mathematically? The questions below will test your knowledge of zero.
If two quantities are added and the sum is zero, what do you know about the quantities?
If you add zero to a number, how does the number change?
If you multiply a number by zero, what do you know about the product?
What is the opposite of zero?
If three numbers have a product of zero, what do you know about at least one of the numbers?
Is zero even or odd?
Answers
Answer:
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Answer:
Step-by-step explanation:
Elementary algebra
The number 0 is the smallest non-negative integer. The natural number following 0 is 1 and no natural number precedes 0. 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).
The number 0 is neither positive nor negative, and is usually displayed as the central number in a number line. It is neither a prime number nor a composite number. 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).[64] Zero is, however, even (i.e. a multiple of 2, as well as being a multiple of any other integer, rational, or real number).
The following are some basic (elementary) rules for dealing with the number 0. These rules apply for any real or complex number x, unless otherwise stated.
Addition: x + 0 = 0 + x = x. That is, 0 is an identity element (or neutral element) with respect to addition.
Subtraction: x − 0 = x and 0 − x = −x.
Multiplication: x · 0 = 0 · x = 0.
Division:
0
/
x
= 0, for nonzero x. But
x
/
0
is undefined, because 0 has no multiplicative inverse (no real number multiplied by 0 produces 1), a consequence of the previous rule.
Exponentiation: x0 =
x
/
x
= 1, except that the case x = 0 may be left undefined in some contexts. For all positive real x, 0x = 0.
The expression
0
/
0
, which may be obtained in an attempt to determine the limit of an expression of the form
f(x)
/
g(x)
as a result of applying the lim operator independently to both operands of the fraction, is a so-called "indeterminate form". That does not simply mean that the limit sought is necessarily undefined; rather, it means that the limit of
f(x)
/
g(x)
, if it exists, must be found by another method, such as l'Hôpital's rule.
The sum of 0 numbers (the empty sum) is 0, and the product of 0 numbers (the empty product) is 1. The factorial 0! evaluates to 1, as a special case of the empty product.