0.999...Does not equal 1

The basicsI would like to begin this round by going over various assumptions that my opponent has made, I would then like to refute and point out con's poor understanding of mathematics and the concept of infinity. Let us start by understanding the difference between rational and irrational decimals. Rational decimals repeat the same digit, thus 0.999.. is an rational decimal. Irrational decimals do not repeat the same digit, pi is an example of an irrational decimal (3.14159..)My opponent has stopped speaking in decimal terms and begun favoring fractions, he fails to realize that irrational numbers, including pi cannot be represented in fractions. This is important to note as this suggests the limitations of fractions to represent an infinite sequence of numbers, which is important to this debate. [A]0.333.. is defined as a string of 3s that increase in value by one tenth the value of the previous 3, this suggests an increase in value that is by definition infinite.1/3 does not increase in value and could only be an accurate representation of splitting an object into 3 equal parts if we could split an object into 3 equal parts without losing any value. 0.333.. is different to 1/3 as it suggests we lose 0.00..1 of value in total. [1] [2]I therefore urge readers to reject my opponents assumptions. Refutation"While I agree that infinity is neither a natural or real number, it is treated as a number in mathematics, particularly calculus, and given these definitions, 0.999... is not infinity, because 0.999... is both a real and rational number and is not greater than any countable number."My opponent here makes numerous contradictions, he even goes so far to suggest that 0.999.. is not an example of infinity as it is not greater than every number. I urge con to prove this by counting from 0.9 to 0.999..Aside from the abundant contradictions. Con believes infinity is only infinity, because it's bigger than any other countable number. Laughable. Infinity is not larger than infinity +1 Therefore it's reasonable to assert an infinity can exist in a value lesser than 1, in this instance , in the form of 0.999.. [P1]It is not possible to subtract specifically a rational infinite decimal from anything, as the rule for rational infinite decimals involves an increase in value by one tenth of the previous digit, the answer to the subtraction would therefore have to be a decrease in value by one tenth of the previous digit, giving us a number that is an irrational number. Thus one could not assert 0.999..-0.333..=0.666.. This is the fatal flaw in my opponents argument. The value of infinite = undefined. [3] Answers to my opponents question:1: Has been marked as [1]2: 1/3 is a fraction and has no properties that repeat. This has been marked under [2] for a full break down.3: Has been marked under [3] Calculators have been programmed to round up or round down. Therefore your argument here is weak.4: You're using fractions here, which as I've explained are different to using the base 10 decimal system. The problem is, the decimal system is known as base 10, which limits certain mathematical equations to represent values through 0 to 9. Using fractions gives us more consistent values. To get an infinite value is essentially to get an error, the error is a tiny one that doesn't ruin the base 10 system entirely, but shows it's not perfect. This doesn't mean we should assume 0.999..=1. If con cannot answer these questions, con must concede. I have very clearly answered all my opponents questions, shown his ignorance on the concept of infinity and I now present him with questions of my own that he must answer.1: 0.999.. follows a pattern, whereby we begin with 0.9, does that equal 1? Does 0.9999 equal 1? Where exactly along the infinite string of 9s do we find the value equal to 1?If you cannot identify that point, then you can't ever truly prove your claim to be true, unless you use tricks that rely on misconceptions of how the properties of infinity work.2: When you consider the diminishing value of the 9s within 0.999.. becoming so infinity small, can you tell me what's the difference between a value being so infinity small and simply not existing?If you can't tell me the difference, then we can assert that infinities have no place in mathematics.3: As we both agree that infinity is not a number, how is it that in one of your algebraic equations, you minus a number with an infinite string from another number of an infinite string to get something other than undefined?I fully expect your only counter argument to involve a semantics based argument, whereby you attempt to separate the word infinity from infinite. I've already disproven this. Please refer to my argument labeled [P1]Con? [A] https://www.mathsisfun.com...Both sides have agreed that Djksp cannot vote on this debate.