Real Numbers Flashcards

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1
Q

What are real numbers?

A

The set of all rational and irrational numbers. This includes integers, fractions, and decimals.

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2
Q

What does it mean for a number to be “less than” another number?

A

It is to the left of the other number on the number line.

0 is less than 1 because it is to the left of 1.

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3
Q

What does it mean for a number to be “greater than” another number?

A

It is to the right of the other number on the number line.

0 is greater than -1 because it is to the right.

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4
Q

What does it mean for a number to be “less than or equal to” a number?

A

That number is to the left of or corresponds to that other number.

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5
Q

What does it mean for a number to be “greater than or equal to” a number?

A

That number is to the right of or corresponds to that other number.

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6
Q

What is an interval?

A

The set of all real numbers between two numbers.

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7
Q

What is an absolute value?

A

The distance of a number from 0 on the number line.

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8
Q

What is the triangle inequality?

A

|r+s| is less than or equal to |r|+|s|

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9
Q

What is a number line?

A

A line with negative numbers to the left of 0 and positive numbers to the right of 0.

Every point on the number line is represented by a real number and vice versa.

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10
Q

What is the distributive rule in mathematics?

A

X(y+z) = xy+ xz

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11
Q

What is the zero product property?

A

Any number multiplied by 0 is 0

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12
Q

What is the Commutative property?

A

x+y = y+x and zy=yz

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13
Q

What is the associative property?

A

(x+y)+z =x+(y+z) and x(yz) = (xy)z

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14
Q

What is the identity property?

A

p*1= p and p+0=p

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15
Q

What are the negation rules?

A

Multiplying a negative times a negative is a positive and multiplying a negative times a positive is a negative

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16
Q

If r is greater than 1, is r^2 greater or less than r?

A

Greater

17
Q

If 0< r<1 is r^2 less than or greater than r?

A

Less than