Infinity – prealgebra

What is Infinity?

Infinity is both a mathematical and a philosophical concept of something being boundless and endless.

Fundamental Skills:

• Understanding infinity is not a number
• Understanding the idea of getting closer and closer to something without ever reaching it

Words to Use:

• Infinity
• Infinte
• Finite
• Infinitesimal
• Limit

Prerequisite Skills:

• None – although it takes some mental maturity to think abstractly about infinity, discussions can be had with preschoolers about God and forever.

Ways to Practice:

Infinity comes up throughout conversation regarding multiple topics, including:

• Numbers
• Number lines
• Parallel lines
• Time
• Space
• God

Getting closer and closer to something without ever reaching it is involved in the ideas of:

• Escape velocity
• Absolute zero

Mathematically, the idea of infinity can be approached by talking about:

• Counting
• A line (vs. a line segment)
• The number line
• The Cartesian plane
• Parallel lines
• Fractions with repeating digits
• Irrational numbers
• Pi
• Dividing by increasingly larger numbers
• Dividing by increasingly smaller numbers
• Discussing how repeated division on a calculator eventually rounds to zero and repeated multiplication leads to an error
• The infinite sum of all of the reciprocals of the powers of 2

Advanced Skills:

• Summation Notation
• Finding Limits

Non-transferable Skills:

• Bigger Infinities
  • Some infinities are bigger than others. Knowing this is not a transferable skill. But discussions about this can often be intriguing to kids. The transferable skill involved with this is understanding how to prove that some infinities are bigger than others. When they (and you) are ready, it can be educational to explain the proof of this. But, without the proof, the idea that some infinities are bigger than others is a trivial, non-transferable idea.

Related Concepts:

• Limits
• Cartesian Coordinates
• Number Line
• Asymptote
• Sets
• Paradoxes