How Far is Infinity?

Young children lay in the grass staring at the sky and start to think about Infinity without even knowing the word. As they move into arithmetic they start to realize that the number system goes on forever. As they advance in their math studies they start to learn that there is positive infinity and negative infinity. They learn that there are an infinite number of points on a number line between zero and one. A lot of the thinking about Infinity becomes mind boggling. Mathematicians discuss such lofty ideas as infinity plus infinity… What does that equal? Can infinity be measured?

If asked “What is calculus?” The shortest answer, I would say, is that calculus is the study of infinity and limits. It is the mathematical study of continuous change. A “limit” tells us the value of a function as its inputs get closer and closer to some number or as the input approaches infinity.

It is generally believed that calculus was discovered independently in the late 17th century by two great mathematicians: Isaac Newton and Gottfried Leibniz. The story is that they discovered calculus simultaneously, not knowing the other was working on the same thing. Then, in the middle of the night many years ago while watching a PBS show, it displayed handwritten letters between the two men and I shouted, “I knew it!” But since that show I’ve not seen it published anywhere else. Maybe a deep internet search might reveal the “truth”.

A metaphor for life that I like to use is:

“Perfection is only approachable, not obtainable” – same thing for “infinity”.



For those who are interested in diving further into the wonders of infinity, please take a look at the Netflix documentary about Infinity called “A Trip to Infinity” released in 2022.

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Opinions and Analysis by: Illana Herzig Weintraub

Publisher: MathMedia Educational Software, Inc.

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