.999... is exactly equal to 1

My opponent has offered little to counter my resolution that '0.999... is exactly equal to 1'. As it stands now, the burdens stand as follows: The task of PRO (myself) is to demonstrate that 0.999... is exactly equal to one. The task of CON (my opponent) is to demonstrate that 0.999... is not exactly equal to one. All my opponent has presented is variations of the phrase 'It doesn't make sense', regardless of the fact that I have shown mathematically that it does make sense. As a guess, I would suggest that my opponent fails to recognise the notion of 0.999... it is not a finite number, it is infinite, it has no end at all. The statement 'it will infinitely be less than one' doesn't make sense because there is no end to this recurring decimal, it does not stop at one particular 9. If it did, then indeed I would be mistaken in my proposal that (as an example) 0.999 is equal to one. Allow me to demonstrate with my previous example, although this time showing why this can only work with recurring nines. x = 0.999 10x = 9.99 10x - x = 9.99 - x 9x = 8.991 x = 0.999 And I am sure from here you can see that indeed 0.999 =/= 1, the same is true for any finite number (except 1 lol), however for infinite recurring decimals it is indeed true that 0.999... is exactly equal to 1. To further expand on my point, allow me to show another example of what I just did. x = 0.9999999 10x = 9.999999 10x - x = 9.999999 - x 9x = 8.9999991 x = 0.9999999 You'll have to forgive me if I forgot a few nines (it was meant to be 7 nines), but the point should be clear by now. The case of 0.999... = 1 is only true for 0.999... Not only that, but the proof also doesn't work for other recurring decimals such as 0.888... x = 0.888... 10x = 8.888... 10x - x = 8.888... - x 9x = 8 x = 8/9 Only for 0.999... does it equal exactly 1. Now, allow me to present a simpler proof of the resolution. I'll do my best to explain each step. 1/3 = 0.333... [Any calculator can confirm this] 3*(1/3) = 3*(0.333...) [brackets added for ease of viewing, both sides are multiplied by three] 3/3 = 0.999... [I bet you can see where this is going] 1 = 0.999... [TADAAAAAA] This proof is much easier for our less mathematically minded voting audience, essentially what it is saying is that one third equals 0.3 recurring, when both sides are multiplied by three, the proof yields 1 = 0.999... some people may be wondering how I can simply multiply an infinitely recurring decimal by a finite number three. The answer is simple, as the 3's in 0.333... never actually end, the multiplication simply consists of making them all nines, of course if it was a finite number I could not do this proof either. It would fail at the very first step. 1/3 = 0.333 [WRONG!] The same proof works for 1/9, for instance 1/9 = 0.111... 9*(1/9) = 9*(0.111...) 9/9 = 0.999... 1 = 0.999... Now my opponent talks bout how 'math isn't perfect' and indeed there are still many paradoxes to be solved, however unless my opponent wishes to disprove rudimentary reasoning and the very basic algebraic processes which are the framework of most mathematical disciplines, then I suggest he attempt to highlight my arithmatic ineptitude. Ladies and Gentlemen, I have thoroughly acheived by burden. The only reasonable vote is PRO. I'll be happy to answer any questions by the voting audience in the comments section. Thank you