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Rational Vs. Irrational Numbers Cartoon


What are we looking at here?

At the top we have a group of famous irrational numbers, φ, π, e and √2. Hiding behind a wall at the bottom we have two fractions. The 1/5 fraction is saying to the 3/4 fraction: "Oh-no... we're outnumbered!"

And... why is this funny?

At the surface level, we have numbers saying they are "outnumbered." This is already funny. Hahahaha... Okay, now that we've composed ourselves, let's explore the depth of the joke here. Back in the time of Pythagoras, people refused to believe that these crazy irrational numbers even existed. Many centuries later, at the end of the 1800's, the German mathematician Georg Cantor made the startling discovery that irrational numbers are actually more numerous than the rationals! It was shocking that there could be more than one kind of infinity. The fractions are "countably infinite" whereas the irrationals are "uncountably infinite." This bigger infinity that you get with irrationals is fascinating... that is, unless you're a fraction just realizing that you are completely outnumbered.

That IS fascinating! Can’t wait for the next Off the Number Line cartoon!

Matthew Peterson and James Huang

About the Author

Matthew Peterson, Ph.D., is Co-founder and Chief Research & Development Officer at the MIND Research Institute. James Huang is Senior Visual Designer at MIND Research Institute.


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