Understanding Rational and Irrational Numbers

What did the Greeks originally believe about numbers?

• All numbers are irrational.

• Numbers are imaginary.

• All numbers are rational.

• Numbers are finite.

What is the significance of the rational number one-half between zero and one?

• It is the only rational number between zero and one.

• It is an example of an infinite number of rational numbers between two integers.

• It is an irrational number.

• It is the largest rational number between zero and one.

How can we prove that there are infinite rational numbers between any two rational numbers?

• By finding a number halfway between them.

• By using a calculator.

• By identifying all irrational numbers between them.

• By counting all integers between them.

What fills the gaps between rational numbers on the number line?

• Irrational numbers

• More rational numbers

• Integers

• Whole numbers

What is the collection of rational and irrational numbers called?

• Imaginary numbers

• Complex numbers

• Real numbers

• Whole numbers

What is the probability of randomly selecting an integer on the number line?

• 0%

• 100%

• 25%

• 50%

Why are the chances of picking a rational number on the number line essentially zero?

• Because irrational numbers are countable.

• Because rational numbers are finite.

• Because there are vastly more irrational numbers than rational numbers.

• Because there are more integers than rational numbers.

What did Georg Cantor prove about infinities?

• Infinities are finite.

• There are different sizes of infinities.

• Infinities do not exist.

• All infinities are the same size.

What type of infinity are irrational numbers considered?

• Imaginary

• Finite

• Uncountable

• Countable

What property of real numbers is essential for calculus?

• They are imaginary.

• They are countable.

• They form a continuum.

• They are finite.