Is 0.999... repeating = 1.0 ?
Debate Rounds (3)
This video states that 0.99999... repeating is equal to 1. Please only respond with your arguments, not the ones from the video because I have already watched the video.
I stand opposing the equality of the two numbers.
The number .999... can be expressed as this sum:
This is a convergent series so, according to the convergence theorem,
This actually uses more 'correct' math than the video, which lies on several assumptions as it is intended for the general populace. However, I extend all arguments presented in the video to my argument as supplementary evidence.
You don't have to write an infinite amount of zeroes, you only have to put the repeat symbol above the 0 to represent the fact that the 0s are infinitely repeating. The 1 is there the whole time
Rational number: a number that can be expressed as a fraction; the decimal form ends/repeats infinitely. 1 is rational, so is 0.999. It's 1's dec. expansion. Is .333 irrational? No, it equals 1/3. The relationship is the same.
You can't prove 0.999 =1 using a mathematical formula.
That's exactly what convergence theorem does, so you CAN apply the formula I gave. These theorems exist so we can rationalize complex problems and establish intrinsic problems of math It is the same thing with limits. These laws are accepted universally.
You don't have to write an infinite amount of zeroes, the 1 is there the whole time
You said that .999 would never reach 1, but now you're saying that 0.000 will eventually reach 0.001. The 1 is not just there, it doesn't exist. To put it in other words, picture the 1 at the end. Put a 0 in front of it. Repeat this infinitely, and you will never find the 1. Before you try to apply this argument to .999, try applying the convergence theorem formula to .000.
F22Raptor forfeited this round.
As I have provided mathematical proof that remains unrefuted, and as my opponent has forfeited Round 3, I extend my arguments and implore at least one person to see this and vote PRO (I don't really want this to end in a tie when it certainly was not).
1 votes has been placed for this debate.
Vote Placed by Mikal 2 years ago
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Reasons for voting decision: FF and just all round a beat down. Con was not able to refute anything pro brought up.
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