0.999... = 1 | Prove Me Wrong

You said "10x - x = 9x -x" in Round 2. Also, it is not at all true that "9x - x is always something less than 10x - x". Simply set x equal to any negative number and you will see that 10x - x is always less than 9x - x. I don't mean to sound like a broken record, but Pro's complete lack of understanding of such basic mathematical concepts as the one(s) that would make obvious the falsity of the statement regarding (9x - x) always being less than (10x - x) is making this quite a difficult conversation.I don't know exactly how else to explain the proof by contradiction that was based on the entire fact that 0.3 + 0.3 != 7. I'd urge you to actually go through the resources I provided as it should be very valuable to you in future debates.I am not sure I at all understand what you mean when you say, "what proof do you have that h exists(?) I could say '1 < h < 1'"The whole point of using a variable like h or x is to illustrate a later contention. Stating that h exists is an assumption, in the mathematical, logical sense, used to prove a point. I take it you did not view the documentation on the proof of derivative differentiation using limits, which is the basis of the entire realm of calculus.If you checked those calculators I gave you, you either used them incorrectly or entered too many 9's. That is not to say there is a given number of 9's that make 0.999... actually equal 1, it's just a limitation of any given calculator. Precision of calculators are specifically defined by the number of digits to which they compute. Given infinitely long precision/computing power, you will never get that result.I don't know if it's fair for you to ask me to watch your "wonderful" video that will "make everything super clear" without you having pursued ANY of the resources I provided, but you did say "please" in all caps 15 times which makes me realize that you are significantly desperate to prove a point with someone else's words that you cannot with your own.Anyway, let's look at each of the "proofs" offered by this video: This is obviously not a proof, it's just offered for people who implicitly accept the claim that 0.999... = 1 This is also not a proof, as the video itself admits (1:11) Reason 3 essentially says that 0.9 repeating is equal to 1 because trying to write a number that is infinitesimally smaller than 1 should not be accomplished by writing 0.9 repeating. This is one of the most basic, egregious logical fallacies known as begging the question. For that reason, I think we need to immediately disregard this point because it is blatantly illogical (1:34) The next reason is the exact same argument you already provided (and subsequently misquoted) which just blatantly insults the institution of algebra by stating that 9.999... minus 0.999... equals 9 and going from there. I don't think any mathematician worth their salt would allow for such an argument in a logical debate The next "bottles of beer" example is invalid for the same reason (3:02) The argument labeled Reason 5 is based on the exact same improper deduction as your first original argument and the one labeled #4 in this list. Not only is it utterly redundant, it is also invalid making it especially difficult to reconcile (3:42) At 4:33 this video directly confirms the existence of "hyperreal numbers" which form some of the basis of calculus. This speaks to the gist of the argument with h that you had trouble grasping. I don't know exactly why they included this as it specifically refutes the rest of their point by saying 0.999... ONLY equals 1 in a particular type of algebra and not in many other sound mathematical domain. As the burden of proof is on Pro, and Pro did not specify a particular mathematical domain in which 0.999 must equal 1, it can only be assumed that they attempted to affirm that 0.999 must equal 1 in ALL domains. Given that they provided a video as evidence specifically stating there are domains in which 0.999 does not equal 1, I feel this is a point of possible forfeiture in and of itself. Still, I feel that the rest of Pro's logic is faulty enough that we need not bring in hyperreals to disprove it I can't help but laugh at Reason 6 as it borrows from the exact same logic as many of the other invalid claims. I don't know why this video is so intent on using such an illogical argument as a basis for all of its "proofs", but I hope I don't have to view any more of these (4:59) Reason 7 befuddles me. It states that no matter how close 2 numbers are, there are still an infinite amount of numbers between them, and an infinite amount of numbers between those, and so on. This explicitly contradicts the logic Pro has used previously and, even more shockingly, contradicts the logic they go on to use a moment later (5:44) Note the 5:57 mark where it is stated, "that is a system where you can have a number infinitely close to 1 but not 1." That comes directly from a video Pro offered as proof using reasons that weren't his/her own and I assume he/she did/does not completely understand them or their flaws. Reason 8 we have already refuted as just plain silly (6:20) Reason 9 brings up the only somewhat-logical point put forth thus far, but makes a gross mischaracterization. The convergent series described in fact DOES NOT equal 1. For that matter, "there is no known number equal to the sum of the series" per the University College of London. Eventually, the video states that the ultimate reason 0.999... equals 1 is "because it works." I must say, I cracked a small laugh while watching this on my computer. Among the many issues here, it is a clear example of circular reasoning. To say something is true because it works when we have also said it works because it's true is, like Reason 8, just plain silly. One of the most common criticisms of science by Christians is that the latter allege that the former feel their arguments "work because they're true." Given that Pro likely belongs to this camp, it seems he/she is trying to have their proverbial cake and eat it to. I'd happily start another debate on the topic of whether things that "work" are always "true". However, I'd ask that Pro refrain from making that a huge, overriding topic of debate here as it is not the issue at large. I understand Pro was unable to defend his/her very own claims after offering many illogical, self-contradictory views. When this happens, it is not uncommon for debaters to try and use other people's words in their own defense. I'm not sure that a YouTube video should qualify as irrefutable proof of anything, but this particular video and its accompanying invalid arguments should definitely not be factored into any intelligent argument. Have a great day!