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Anonymous
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does 0.9999999.......... equal 1

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 Voting Style: Open Point System: 7 Point Started: 7/14/2018 Category: Philosophy Updated: 3 years ago Status: Debating Period Viewed: 772 times Debate No: 116576
Debate Rounds (4)

20 comments have been posted on this debate. Showing 1 through 10 records.
Posted by A1DS 3 years ago
No it's not because 0.999... isn't infinity, it's a real number (see previous comment). The key distinction is the infinite repeating digits are after the decimal place instead of before it, and therefore 0.999... doesn't fit the definition of infinity as I can list a number (e.g. 2) which is larger than 0.999... so it's an entirely different scenario. In the case of infinity, it is impossible to list a number of greater value, so clearly 0.999... represents a different scenario.
Posted by DeletedUser 3 years ago
But the thing is your equation was doing the exact same thing
Posted by A1DS 3 years ago
Which, by definition makes it infinity, so you cannot manipulate it with the algebra you have been trying to use. You'll never see a proper, valid mathematical proof using ...X.Y because it's not essential, any such "number" (and I use that term loosely because infinity is a more of a concept than a number) can be represented as infinity. Your algebra isn't actually mathematically valid.
Posted by DeletedUser 3 years ago
I didn't mean "add an infinite string of 9's to it". I meant right out the rest of the number which happens in this case to be an infinite string of 9's.
Posted by A1DS 3 years ago
It may help you to look into what constitutes, real, rational and irrational numbers. Rational numbers is the set of numbers that can be represented by an integer fraction. 0.999... falls into this category as it can be represented by 9/9 (which is equal to 1 funnily enough). Irrational numbers cannot be represented this way, and include examples such as pi and the square root of 2. Both of these can include examples of numbers with an infinite number of decimals places. Such as 0.333... and 0.999... from the rational numbers and both of the aforementioned examples for the irrationals. Together, the rational and irrational numbers form a set that we refer to as the real numbers. You can google the mathematical axioms on which the reals are defined if you'd like to learn more, but they get quite complicated quite quickly.
Posted by A1DS 3 years ago
Reflectively, I think where your problem is actually coming from Masterful is you don't know what a real number is. Something with an infinite number of decimals is still a real number. Pi is a real number, the square root of 2 is a real number, just because decimals go on infinitely doesn't mean these numbers behave like infinity. So while you've correctly identified that infinity is a concept rather than a number, you're incorrectly applying that same assumption to real numbers.

Hope this clears things up for you.
Posted by A1DS 3 years ago
Limit theory* sorry I ran out of characters.
Posted by A1DS 3 years ago
Okay so first I'm going to address what jackgilbert had to say:

You can't just "add an infinite string of nines to the left" it's not mathematically valid. Any such number with an infinite string of non-zero digits "to the left" is just represented as infinity. Your maths doesn't hold up because you fail to realise that infinity is a concept, not a number, so the algebraic techniques you're attempting to apply to it don't work. I'll wager the person who made that video actually doesn't have a particularly good understanding of mathematics because what he's doing is wrong.

Both examples are exactly the same as both are just equal to infinity. In neither case is your algebra consistent because in neither case are you correctly applying algebraic principles to actual 'numbers', you can consider it like trying to multiply "limit" by 10, this is obviously nonsensical because you cannot multiply a concept by 10.

0.999... isn't infinity? It does not behave like infinity and is a real number. I can say 0.999... is less than 2 and more than 0.9. I can use it in equations, I can apply a variety of completely valid operations to it precisely because it is a real number. I'm not entirely sure what your argument is and it seems largely nonsensical to me. First of all "this truth" does not create horrors for those who believe 0.999...=1, quite conversely it is essential for proving it, and I'd suggest entirely contradictory to your statement, the vast majority of people who recognise 0.999...=1 will do so on the basis of a firm understanding of mathematics, including this concept of infinity. I think you misunderstand what a real number is? Real numbers include basically any number that isn't the square root of a negative (the imaginary numbers). So the irrational numbers (like pi), integers etc. are all considered real numbers.

Hope this has cleared things up, but I think the best thing for you guys is to at limi
Posted by DeletedUser 3 years ago
x=........99999999.9999999..........
Multiply both sides by ten we get
10x=........99999999.9999999......
We get exactly the same number as before because infinity goes on forever in both ways. This proves that if you multiply infinity by 10 it does nothing
10x=x
9x=0
x=0
The funny thing is it is actually consistent with the other equations because the algebra is telling me .......99999999 is -1 and 0.999999..... is 1 and .......999999999.9999999....... is 0 so 1+-1=0.
Posted by DeletedUser 3 years ago
the original x is infinitely many 9's going off to the left. Multiplying it by ten takes the last 9 away and replaces it with 0. Infinity times 10 is still infinity. Let me right out an equation for you

x=..........9999999999
Multiply both sides by 10
10x=........99999999990
But look at ....9999990. It is exactly the same as the original x except minus the final 9.
10x=x-9
9x=-9
x=-1
It is exactly the same thing you did with your equation.
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