0.999...Does not equal 1

Though not very direct, thanks for your last round, Pro.Pro either dodged or spun answers to my questions.Figures.Well, let's remedy all of that garbage.*Questions From Round 2*1. I had asked Pro what the difference was between the product of 3 times 1/3 and the product of 3 times 0.333...Pro responds:"0.333.. is defined as a string of 3s that increase in value...1/3 does not increase in value...0.333...is different to 1/3 as it suggests we lose 0.00..1 of value in total."My response:Opt-in voters, pay attention.I had asked about the difference between the PRODUCTS of 3 times 1/3 and 3 times 0.333... and Pro responds with how 1/3 and 0.333... have different values (take any calculator and divide 1 by 3 and you will ALWAYS get 0.333... they are the same) without ever mentioning the products of the two sets of factors I asked about.By not directly responding to the question posed in the 2nd round, Pro concedes that the products of those two sets of factors are in fact equal thereby equating 1/3 and 0.333...2. I had also asked Pro WHY we can use arithmetic with infinitely repeating decimals, like 0.333... (1/3).Pro responds:"1/3 is a fraction and has no properties that repeat."My response:Wow!1/3 means "one divided by three."You cannot divide 1 by 3 without "properties that repeat."You do know that a fraction is just the numerator divided by the denominator, right?Therefore, 1/3 = 0.333...Also, this "response" does not address why it is that we can use infinite decimals in arithmetic.Boo Pro.3. I had asked Pro if you can ever DIVIDE by 3 without MULTIPLYING by 0.333...Pro responds:"It is not possible to subtract specifically a rational infinite decimal from anything."My response:Readers, I had asked about DIVISION and MULTIPLICATION, not subtraction, obvious dodge by Pro, and though irrelevant to my question, Pro's wrong here too, infinite decimals can be subtracted from numbers.https://www.dpmms.cam.ac.uk...Pro adds:"Calculators have been programmed to round up or round down."My response:Red herring.Readers, take a calculator and divide 1 by 3.Take THAT answer and multiply it by 10.Now, take 10 and divide by 3.The answers are identical AND not rounded!Boom.Multiplying by 0.333... is the same as multiplying by 1/3.4. I directly asked Pro if he could see how 3 times 1/3 must necessarily involve an infinite decimal in both the factor and the product.Pro responds:"You're using fractions here, which as I've explained are different to using the base 10 decimal system."My response:All fractions equal a rational decimal, like 0.333... or 0.999... and "decimals are rightfully restored as fractions of a special kind..."https://math.berkeley.edu...Pro asks:"Where exactly along the infinite string of 9s do we find the value equal to 1?"My response:When you subtract a number from itself, the result is zero. For instance, 4 " 4 = 0. So what is the result when you subtract 0.999... from 1? Without an infinite decimal, you get:1.0 - 0.9 = 0.11.00 - 0.99 = 0.011.000 - 0.999 = 0.0011.0000 - 0.9999 = 0.00011.00000 - 0.99999 = 0.00001Then what about 1.000... " 0.999...? You'll get an infinite string of zeroes. What about that '1' at the end?Ah, 0.999... is an infinite decimal; there is no "end", and thus there is no "1 at the end". The zeroes go on forever. And 0.000... = 0.http://www.purplemath.com...*Conclusion*Man that was a thorough refute.How's that for only 30 minutes?Voters, 0.999... = 1 and Pro has done nothing to show otherwise...just a lot of dodging facts.