The Truth About the Most Controversial "Number"
For centuries, humans have argued about whether 0.999 (repeating) = 1, and there are still many misconceptions on BOTH sides of that debate. In this extra-long episode, I’ll take you on a journey through infinite decimals to help clear some things up
Most of this episode is mathematical demonstrations, but there is also a philosophical edge to this topic, so leave a comment letting me know your personal opinions/beliefs about this "number" (hopefully after watching this whole episode to see all of the misconceptions I cover). And/or leave a comment if you can count how many squirrels appear in this episode haha.
A few clarifications:
-- For the definition of the Archimedean property, I accidentally spelled it Archimedian, and also I should have clarified that the numbers should be positive and that n should be an integer.
-- I mentioned the commutative and associative properties just as recognizable examples of properties that humans take for granted about the real numbers, which can sometimes be lost when switching systems. They are not specifically the properties that are lost by the hyperreal or surreal systems I mentioned (if/when I make an episode about those systems in the future, I’ll clarify more about which properties become more difficult in those).
-- When I said that every terminating decimal has two representations, I should have added "non-zero" since zero is technically terminating but doesn't have the same type of alternate form.
-- Some comments thought that I shouldn't have used "controversial" as a description and claimed that nobody disagrees about this topic nowadays. Let's appreciate the irony of people arguing that nobody is arguing haha. If you look at the comments of this video, you can see that it's clearly still a topic many people disagree/debate about.
Make sure you're also tuned in to my @Domotro channel for my livestreams, shorts, and other bonus content!
This episode was filmed by Carlo Trappenberg, and was directed / edited / soundtracked by me (Domotro).
Special thanks to Evan Clark and to all of my Patreon supporters:
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Domotro
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In case anybody searches any of these terms, some topics mentioned in this episode include: 0.9999999 (0.9 repeating / zero point infinite nines) and whether that = 1, repeating decimals, patterns in different numeral bases, what consists of a proof vs. a demonstration, properties of the real numbers such as the commutative and associative properties, the hyperreal and surreal numbers, infinitesimal numbers represented by epsilon, the philosophy of why numbers are useful, fractions vs. decimals, irrational numbers like pi, multiple representations of numbers in bases, and more...
Disclaimer: Do NOT copy any dangerous-seeming actions (which were actually performed in a careful way) involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is for education and entertainment.
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