In the case of an infinite decimal, again standing in for the kind of infinite sequence of terminating decimals we saw above, we identify the sequence with its limit.
This is what we mean when we say that 0. The same idea works for any rational number with a repeating infinite decimal expansion.
Something similar happens with irrational numbers that have non-repeating decimal expansions. In general, any infinitely long decimal expansion is thought of as the limit of the sequence of terminating decimals that make up the infinite expansion. So, the reason why 0. For you. World globe An icon of the world globe, indicating different international options. Get the Insider App.
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It often indicates a user profile. Connect and share knowledge within a single location that is structured and easy to search. This occured to me while I discussion on one of Zeno's Paradoxes. We were talking about one potential solution to the race between Achilles and the Tortoise, one of Zeno's Paradoxes. However, this isn't that case, as, no matter how many ones you add, 0.
The problematic part of the question is "no matter how many ones you add, 0. I give here a proof and tou can see Does. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Is 1 divided by 3 equal to 0. Asked 8 years, 8 months ago. Active 5 years, 8 months ago. Argument from algebra: The expression 0. Call this numerical value " x ", so 0.
Multiply this equation by ten:. There is no "end" after which to put that zero. Argument from semantics: A common objection is that, while 0. But what is meant by "gets arbitrarily close"? It's not like the number is moving at all; it is what it is, and it just sits there, looking at you. It doesn't "come" or "go" or "move" or "get close" to anything.
On the other hand, the terms of the associated sequence, 0. No matter how small you want that difference to be, I can find a term where the difference is even smaller. This "getting arbitrarily close" process refers to something called "limits".
You'll learn about limits later, probably in calculus. And, according to limit theory, "getting arbitrarily close" means that they're equal: 0. Note regarding all of the above: To a certain extent, each of these arguments depends on a basic foundational doctrine of mathematics called "The Axiom of Choice".
A discussion of the Axiom of Choice is well beyond anything we could cover here, and is something that most mathematicians simply take on faith.
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