It doesn’t change anything about the point of this post, but it is does make some of the statements I made technically untrue. It primarily happens when one allows certain types of infinitesimals to exist but not others. One can design axioms which allow for infinitesimals to exist yet have those two numbers be equal. The only real area of disagreement is it points out there are frameworks which allow for infinitesimals where the two numbers are still equal. It openly states there are algebraic frameworks in which 0.999 does not equal one. I’ve suggested he could comment here to explain, but in the meantime, I feel I should point out the link he presented largely agrees with me. I have no idea what he thinks is wrong with this post. You need to begin by understanding what the textual string “0.999…” represents this is by no means trivial. I’m very doubtful you have enough maths to even begin to understand why. I’m not sure he’ll want to comment here, so I’m copying what he said so people can see his disagreement: Credit where credit is due, and whatnot.Ĭonnolley takes issue with this post. As such, I felt it was appropriate to share a link to this post over there. I wrote this post because of a (in-person) discussion which stemmed from an offhand comment I made about an offhand remark in a comment by William Connolley on this blog post. Which answer is “right” just depends on which type of math you feel most comfortable with. If you feel it does equal one, you’re right too. If you feel 0.999… does not equal 1, you’re right. Namely, they don’t know what they’re talking about. “Proofs” the two are equal tell us nothing about the subject but everything about the speaker. It’s tricking people by assuming there could be no difference between the two numbers then concluding there is no difference between the two numbers.Īnyone who understands how math works should know 0.999… equals 1 only if you choose for it to. Implicit in all of them is the statement, “Using the real number system.” That’s begging the question. Whether 0.999… and 1 are equal is based on the completely arbitrary choice of whether one uses the real number system or a different one.Īll the “proofs” the two are equal are meaningless. Which one you use is merely a matter of preference. ![]() It’s just as valid as the real number system. There’s an entire field of math which uses infinitesimals. They’d use a different one, like many mathematicians who work with infinitesimals on a regular basis. A person who thinks 0.999… doesn’t equal 1 obviously believes infinitesimals exist. One axiom underlying the real number system basically says: It’s a statement assumed to be true without proof. You see, there is a thing in math called an axiom. Why then do so many people believe they are? Because they say so. When we do that, we see there is a difference – 0.000…1. If the two are equal to one another, subtracting one from the other must give an answer of 0. The reality is no “proof” can address the issue better than simply looking at the two values. It’s just an optical illusion relying on tricking the reader by hoping they don’t notice the hand-waving. How does one multiply an infinite series of 9s by 10? What happens to the zero you’d get when multiplying by ten? Are we to believe it just disappears? Consider this common “proof” the two equal one another. That’s a harsh comment, but I think it’s fair. People who offer “proofs” otherwise don’t understand math.
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