It is NOT a nooby thing to optimize for maintainability, simplicity, and readability!

÷ and / mean the same thing.

bonehead: "As a middleschool [sic] math," Except you do not accept middle school math - you flatly disagree with it. bonehead: " i have been trying to learn for about a year as to why most maths believe that ".99..." is 1, using limited resources such as math books and comments in KZbin videos." You have not been trying to learn. You have only been troIIing. You ignore everything you read and just arbitrarily say the mathematicians are wrong. bonehead: "I initially thought math was stretching the meaning of equal to equivalent." You do not know what the meanings of "equivalent" or "equal" is to a mathematician. bonehead: "Wrong! Math is saying ".99..." is 1 using formulas and limits." That's right. Well done. bonehead: "The video points out problems in using infinite repeating decimals in calculations." Nope. It is saying there are problems if you don't define what the sum of an infinite decimal is. bonehead: "At one point saying in the video that you can never finish any calculation on infinite decimals." Timestamp please. If he did say that, he was referring to numerical computations. i.e. you cannot literally start with 0.9, say, and then append one 9 at a time, as that computation (process) will never finish. It will never get to 0.999.... bonehead: " (I believe that a limited amount of "calculations" can be used, such as adding ".11..." + ".88..." = ".99..." . But adding ".11.. " and ".99..." is problematic in basic addition. What is ".11..." in the first place.)" Beliefs, especially yours, have no place in mathematics. 0.111... + 0.999... = 1.111.... The value of 0.111... is the limit of the sequence 0.1, 0.11, 0.111, ... and that is easy to prove is equal to 1/9. The fact that you can do these things is allowed because of a few theorems regarding infinite series. Such as: Theorem: If a_1 + a_2 + a_3 + ... and b_1 + b_2 + b_3 + ... are convergent series, then (a_1 + a_2 + a_3 + ...) + (b_1 + b_2 + b_3 + ...) = If (a_1 + b_1) + (a_2 + b_2) + (a_3 + b_3) + ... bonehead: "In answer to "Does ⅓ = .33... ? NO and yes. ⅓ > ".33..." ," Both those statements are false, and that is why you have never attempted to prove them. They both also contradict what is taught at every middles scohol on the planet. bonehead: " but ".33..." is the incomplete division of 1 by 3." Despite many requests, you have never explained what that twaddle is supposed to mean. bonehead: "( I can agree that ".33..." * 3 could be stretched to be ".99..."" Your agreement is of no importance. Besides, you randomly change your mind about it. bonehead: " but would be <1 ." So you keep on asserting but never proving. bonehead: "10 * ".99..." cant be done by multiplication or addition." Liar. bonehead: "The shortcut of moving the decimal point cant be done without verification of adding 10 times which is multiplication. )" You have seen that verification being done many times, and you know it. Here it is again, for at least the fiftieth time. 10 * 0.999... = 10 * (0.9 + 0.09 + 0.009 + 0.0009 + ...) = 10 * 0.9 + 10 * 0.09 + 10 * 0.009 + 10 * 0.0009 + ... (there is a theorem for that) = 9 + 0.9 + 0.09 + 0.009 + ... = 9.999... bonehead: "The video then goes to the "sum" of the infinite series. There is no exact sum to an infinite series of >0 terms even if the limit of 1/x=0 as x approaches infinity. (Limits don't necessarily equal the entity they refer to)" As usual, you have made no attempt to prove your claim because you know that it is pure BS for the purpose of troIIing. The exact sum of 0.999... actually is 1. bonehead: "Finally it is a choice." That's true. But you don't know what it actually means or what the alternative(s) are. bonehead: "A bad choice ignoring centuries of basic math education." You couldn't be more wrong. It is easily the best choice and it follows from centuries of mathematics. bonehead: " (In another video the math says that in order to say that ".99..." is 1, "you have to give up something"." You are deliberately misrepresenting the fact that it is NOT choosing 0.999... = 1 that would involve giving up algebra (which means things like saying 10 * 0.999... = 9.999...). i.e. you end up with a nightmare. bonehead: " No you dont, ".99..." has a limit of 1," LOL. You make that same idiotic claim about once a week. One year plus and you still don't know what sums, limits, series or sequences are. 0.999... does not a have a limit. It has a sum. That sum is the limit of the sequence 0.9, 0.99, 0.999, .... You seem to think that somehow that sequence is the series 0.999... bonehead: "You could say ".99..." is a set of numbers using the greatest finite number of 9s [0.99..9, 1 ) )" YOU could say it, but you are a clueless deIusionaI troIIing muppet. What ion Earth is "[0.99..9, 1 )" supposed to mean? bonehead: "A real number is unique and precise." LOL. That's one of your favourite nonsensical mantras. bonehead: "A integer has no non-zero digits to the right of the decimal point." Where's your proof of that lie? bonehead: "A rational number is the ratio of 2 integers. (".99..." would not be rational if it was a real number)" 0.999... = 9/9. You have had that prove to you hundreds of times. bonehead: "So far, I have concluded that maths use of the concept of infinity is faulty." That's because you are a clueless deIusionaI muppet. bonehead: "The valuable concept of infinity is dangerous, incomplete, inconsistent and imprecise." That is your favourite meaningless mantra. bonehead: "Always willing to learn." That's a funny way to spell "troII". You are incapable of learning this simple math.

You were not paying attention to what James said. He did not say that 0.999... approaches 1. What James effectively said is that the sequence 0.9, 0.99, 0.999, ... approaches (i.e. gets arbitrarily closer to) both 0.999... and 1 as you step through it. Both [the value of] 0.999... and 1 are THE unique smallest number that is greater than every term in the sequence 0.9, 0.99, 0.999, .... That is why 0.999... = 1. You are confusing that sequence with the series 0.999... (as that is just a concise notation for 0.9 + 0.09 + 0.009 + ...). [the value of] 0.999... := lim n->oo 0.999...9 (n 9s) = limn n->oo 1 - 1/10^n = 1. It really is that simple.

It's not the math that doesn't fit common sense, it's the stupid mathematicians. "The number a approaches b, therefore a = b" is nothing but complete nonsense. Getting closer to something doesn't mean being the same as it. With this stupid logic, they should not be able to take functions' limits at points where they are undefined.

@@saityusufbulur3366 You have not understood the video. Numbers don't approach anything as that would require that they are changing. 2 can't change to another number. What James effectively said is that the sequence 0.9, 0.99, 0.999, ... approaches (i.e. gets arbitrarily closer to) both 0.999... and 1 as you step through it.

KC is really stepping in it. Good job. Math starts their args by saying ".99..." is 1. Then all the proofs work..

​@@johnlabonte-ch5ul LOL. That's right, I am stepping on you. OTOH that's wrong, math does not start by saying 0.999... = 1. It starts by defining the limit of a sequence and the sum of a series. Both are very general definitions and aren't specifically aimed at decimals. For example they cover general Taylor series and much more. Here they are: Limit: Let {S_n} be a sequence of real numbers and let S be a real number. Then S = lim n->oo S_n means that for every real ε > 0 there is a natural N such that for every natural n > N that |S_n - S| < ε. Sum: The sum of a series is the limit of the sequence of its partial sums (if the limit exists). Combining those we get: [the sum of] 0.999... := lim n->oo 0.999...9 (n 9s) = lim n->oo 1 - 1/10^n = 1 Now I'll prove the last equality. Choose an arbitrary ε > 0 and a natural N such that 1/10^N < ε. (The Archimedean property of the reals guarantees that can be done). Then for every natural n > N we have |(1 - 1/10^n) - 1| = 1/10^n < 1/10^N < ε. Because the choice of ε was arbitrary, that must be true for every ε > 0. Therefore the limit is 1. I'm sure that you won't have understood about 90% of this comment. That's because you are a clueless mentaIIy iII muppet.