Basic properties of real numbers Flashcards
Section 1. Very short (29 cards)
For any real numbers x, y, and z, x * (y + z) = x * y + x * z
The distributive law/distributive property
What is the sum of any two real numbers
A real number
The zero product property
x * y = 0 If and only if x=0 and/or y=0
What is the only real number without a multiplicative inverse
0
The multiplicative inverse of x
The number that when multiplied to x equals 1. denoted as x ^ (-1)
The number that when added to x equals 0. denoted as -x
The additive inverse of x
What is an integer
all numbers that only have a whole value part. Ex 42, 24, -13, 12
If x<y then what can we conclude about the relationship between z+x and y+z
z + x<y + z
True or False. any integer is a rational number
True. the ratio of any integer and 1 is the integer
If x<y and y<z what can we conclude aboout the relationship between x and z
x<z
Whats the communitive law of multiplication
For any real numbers x, and y, x * y = y * x
irrational numbers
A number that can not be written as a ratio of two integers. Ex. pi, e, phi, sqrt(2), 74.134531….
What is the only real number y such that x+y=x
0
if x<y and 0>z then which is bigger xz or yz
xy
True or False. The sum of two irrational numbers is always irrational
False, The sum of two irrational numbers can be rational Ex. 53.134531….+ (-3.134531….) = 50
A number that can be written as a ratio of two intigers. Ex. 5/6, -6/7. -142124/9, -5/1
Rational numbers
Rational numbers
A number that can be written as a ratio of two intigers. Ex. 5/6, -6/7. -142124/9, -5/1
The additive inverse of x
The number that when added to x equals 0. denoted as -x
A number that can not be written as a ratio of two integers. Ex. pi, e, phi, sqrt(2), 74.134531….
irrational numbers
What is the product of any two real numbers
A real number
What is the only real number y such that x*y=x
1
The distributive law/distributive property
For any real numbers x, y, and z, x * (y + z) = x * y + x * z
if x<y and 0=z then which is bigger xz or yz
there equal
The number that when multiplied to x equals 1. denoted as x ^ (-1)
The multiplicative inverse of x
