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RECOGNIZING ZERO AND ONE
Jump right to the exercises!
The concepts for this exercise are summarized below.
For a complete discussion, read the text.
SPECIAL PROPERTIES OF 0 and 1
For all real numbers x ,
x+(-x
)=0 .
A number added to its opposite always gives zero.
The "opposite" of a number is also called the "additive inverse".
For all real numbers x ,
x⋅0=
0 .
Any number multiplied by zero gives zero.
For all nonzero real numbers x ,
xx
=x⋅1
x=1
.
A nonzero number divided by itself (or multiplied by its reciprocal) always gives one.
The number
1x
is called the "reciprocal of x" or the "multiplicative inverse of
x";
multiplying a number by its reciprocal gives the number 1 .
Every nonzero number has a reciprocal; zero does not have a reciprocal.
Be on the lookout for these special names for zero and one!
EXAMPLES:
Decide if the given number is 0 , 1 , or a different number:
13
+(-
13
)
Answer: 0
0⋅1
3
Answer: 0
-2⋅
-12
Answer: 1
1/7
1/7
Answer: 1
3
(-1
3)
Answer: not 0, and not 1