Sets: Infinity

The video explores the concept of infinity, starting with the early Greeks' paradoxical understanding and moving to the 17th-century European mathematicians who used it to develop calculus. It distinguishes between countable infinity (LF0) and uncountable infinity (LF1), explaining how some infinite sets cannot be counted, such as the set of decimals between zero and one. The continuum hypothesis suggests LF1 represents the number of points in the universe or moments in time.

What paradox did the early Greeks face when considering the concept of infinity?

• Infinity is larger than any number.

• Infinity cannot be divided.

• Infinity is the same as zero.

• A man can never leave a room if he must cover half the distance each time.

What mathematical branch did European mathematicians develop using the concept of infinity?

• Calculus

• Geometry

• Algebra

• Trigonometry

What is the term for a set that can be put in one-to-one correspondence with natural numbers?

• Uncountable set

• Finite set

• Empty set

• Countable infinity

How can you create a number not on a list of infinitely long decimals between zero and one?

• By making each digit different from the corresponding digit of the numbers on the list

• By changing each digit to zero

• By multiplying each digit by two

• By adding a new digit at the end

What does the continuum hypothesis relate to in terms of uncountable infinity?

• The number of stars in the sky

• The number of points in the universe

• The number of atoms in a molecule

• The number of grains of sand on a beach