.999... is equivalent to 1
Debate Rounds (4)
1. No semantics, kritiks, or trolling.
R1: Acceptance. Con can ask to clarify terms, but cannot make new arguments.
R4: Closing remarks. No new arguments in R4.
Hello, vi_spex. Thanks for accepting! However, let's remember that Round 1 is fo acceptance, so I'm not going to address the argument made there until a bit later.
I'm just going to jump in, demonsrating a few proofs that the mathematical value of .999... is equivalent to the mathematical value of 1.
A Proof by Geometric Series
This proof is actually utililzed in the link that someone posted in the comments.
First, we expand .999... as .9 + .09 + .009 + ...
We notice that an equivalent way to show this expansion is:
9/10 + 9/100 + 9/1000 + ....
9/10 + 9/10 * (1/10) + 9/10 * (1/10)^2 + ....
This is now clearly recognizable as a geometric series, with the first term a = 9/10 and the common ration, r = 1/10. Since the absolute value of r is less than one, we can use a special formula to calculate the sum of the entire infinite series:
Sum = a * [ 1 / (1-r) ]
Plugging in, we see:
.999... = (9/10) * [ 1 / (9/10) ] = (9/10) * (10/9) = 1
A More Common Proof
This proof is perhaps one of the most utilized proofs in demonstrating that .999... is equivalent to 1.
Let x = .999...
We can multiply each side by 10, which effectively moves the decimal place in .999...:
10x = 9.999...
Now we can subtract 1x from both sides:
10x - x = 9.999... - .999... =
9x = 9
By simply dividing both sides by nine, we see that:
9/9x = 9/9 =
x = 1
There are quite a few more proofs on this issue, but I will reserve those for later, based upon what my opponent has to offer. I'd like to remind my opponent that this is a mathematical issue, so he would be wise to approach it in a way that is mathematically sound and utterly devoid of metaphors.
destruction is impossible in reality, rock is rock
To start, the opponent did not attempt to refute my arguments and merely addresses one of them with an ill-formed metaphor.
To answer my opponents question, "what are you expanding, how do you expand a stone?":
I am expanding a mathematical expression. I did not claim to expand a stone, nor do I wish to learn how to expand a stone.
As for his claims about destruction, those aren't relevent here.
Vi_Spex, I specifically said there was to be no trolling. Please use the next round to produce more serious arguments.
I don't think troll debates are fundementally bad. They can often produce some great comedy. However, I made it clear in Round 1 that trolling was a direct violation of the rules. I should be awarded the full 7 points for this debate because of this rule violation.
However, in the off scenario that my opponent isn't trolling and that he is simply being...him... I will address what he has said.
My opponent has claimed he has the ability to expand a unicorn, by which he means change it. However, he has not sufficiently proven the existence of unicorns, thus leading us to believe that vi_spex cannot change what does not exist.
Additionally, he stated that he could not pick the unicorn up from the floor. This is entirely opinionated, as the opponent has likely never seen a unicorn. For all he knows, if a unicorn exists, it may be very light. In fact, the unicorn might only be slightly heavier than air; so light that even a mouse could pick it up off the floor. There is no way of knowing without adequate proof.
Also, the opponent's comment is irrelevant to the debate.
I have demonstrated that .999... is equivalent to 1. These arguments were not contended.
I have also heard that winning a debate against vi_spex actually lowers your ELO. I imagine that this is poetic justice, as I mentioned in the comments that I created this debate because I thought it would be an easy win. I didn't even consider the fact that a win could actually hurt my rankings. If that was your intent in debating me vi, well done. Point made. I'll have to create a minimum ELO for acceptance with my next debates.
so pick up 0.999 stone
1 votes has been placed for this debate.
Vote Placed by logical-master123 1 year ago
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Reasons for voting decision: Okay first of all Con trolled. He had bad spelling too. 2 points to go to Pro.
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