If you have a set of scales and you have a thing that shows on the scale that it weighs two, and another if that thing, that also shows on the scale that it weighs two, and you weigh both together you still see that it weighs five. That's the point.
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It is generally understood, although not necessarily accurately, that the number "2" means "2.000...", that is the number two with an infinite set of zeroes after the decimal.
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(As an aside this is also exactly the same as a number one with an infinite sequence of nines after the decimal.)
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Not exactly.
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Replying to @JustCanadian7 @phyphor and
Yes, exactly. 1.99999999999999... means the limit of the series 1+0.9+0.09+0.009+0.0009+...., which is 2.
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Replying to @JustCanadian7 @IMJackRudd and
Well this is ironic I mean, sure, no one can force you to accept this as true if you don't want to -- that's the whole point of this conversation! Everyone has their own idiosyncratic language about numbers they use on their head to understand the world and that's fine!
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Replying to @arthur_affect @JustCanadian7 and
But from the point of view of standard, accepted, classroom mathematics you're just wrong 0.9999... = 1 is, according to the normal rules, true You can get into an extremely formal proof of it via real analysis, but you can demonstrate it informally with simple algebra
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Replying to @arthur_affect @JustCanadian7 and
My math class are far away but, the way I interpret that is : as 0.3333... is exactly 1/3, 0.9999... is exactly 3/3, or 1.
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Replying to @Dominic11B4 @JustCanadian7 and
Yeah but that's not a rigorous proof because you haven't actually proven that 0.3333... is 1/3 either What this fight is about at heart is whether you're "allowed" to write numbers with that "..." after them and talk about an infinite series of digits
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That said, it's a good *demonstration*, because people typically aren't nearly as intuitively resistant to the assertion that 0.3333... = 1/3 as they are 0.9999... = 1, even though they are, as you say, equivalent
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Replying to @arthur_affect @JustCanadian7 and
If you want to get right to the meat of the issue you don't need the 1/3 Just point out that 0.99999... and 1.0000... are two ways to say the same thing If 1.0000... is "allowed" to = 1 then so is 0.99999...
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Replying to @arthur_affect @JustCanadian7 and
I think an intuitive obstacle to understanding this is that most people are familiar with something that resemble that, it's impossible for a particle with mass to reach the speed of light. So, in physics, you can get close to c but, never reach it. In maths, infinity exists
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