Remomeister

Don’t misquote us. We say 0.333… is infinite, not infinity. Now, if you think you can multiply an infinite number by any number, just because you can do so with finite numbers, I’ll ask you what I asked Dr. D. What is 0.333… times 4? It can’t be multiplied because in our system, multiplication begins with the furthest digit to the right. When there is no furthest digit to the right, multiplication is not possible. You have a syntax error, an illegal operation. Not quite. We said right from the start, that 1/3 does Not equal 0.333… and some of you agreed at one point that you must always “carry the one”. One divided by three then equals 1/3. (That little slash between the “1” and the “3” means “divided by”). Therefore, One divided by three equals 0.333...AND ONE THIRD (also known as “remainder one”). You people keep dropping off an essential mathematical element to get your phony 0.999… argument which drops the “remainder one”, three times. That assertion is absolutely incorrect! 0.3+0.03+0.003+...does=0.333… But does NOT equal 1/3. Don’t misquote us!

Up to this point, you are absolutely correct. Just as 100 divided by 3 equals 33 and one third. 10 divided by 3 equals 3 and one third. 1 divided by 3 equals .3 and one third. In place of “and one third” you can say, “remainder one”. When you have an infinite string such as .333… , you technically drop the “and one third” part of the problem. If you try to multiply your infinite string of .333… by 3, (if it were possible to multiply an infinite string), you would get an infinite string of nines after the decimal. Then you contradict yourself. In order to equal 1.0, you have to start your problem by acknowledging the “and one third”. Therefore, .333…and one third, times 3, equals .999…and three thirds. Tah dah, you now have something that does indeed equal 1.0 just as Nmenth pointed out in his proofs way back on page one of this topic, and just as you yourself admitted to in the first part of your tirade. .999… does not equal 1.0, but .999…and three thirds does equal 1.0 plain and simple. (Inferno, above, is absolutly correct)!

There are always two sides to every argument. Both sides will defend their position to the death, no matter how you prove the other side wrong. If I drop a rubber ball from 12 meters, it drops, hits the ground and ascends to 6 meters, drops, hits the ground and ascends to 3 meters, etc. there will be those who are foolish enough to argue that the ball will be bouncing forever, always half of its previous height. Those with true intelligence, will not base foolish opinions on what others have attempted to convince them, but will use true logic. Hence, if that same ball were dropped from 12 meters and it took 2 seconds to travel down to the ground and back to the acme of 6 meters, then 1 second to drop to the ground and bounce back to 3 meters, etc. it is quite obvious that the ball will stop bouncing before it ever gets to 4 seconds, a far cry from bouncing forever. If you have one pie, and three hungry mates to share it, they will readily slice the pie into three thirds, and all will be satisfied. However, if someone were to say it must be divided exactly decimally, two mates would probably punch his lights out and cut it in half. In other words, fractions are real, and decimals are mathematical imaginations. Cutting a pie into thirds is practical and useful, but where would one find practicality in dividing something into three .333... pieces? You won't be stopping within one crumb, one grain of sugar, one molecule of fruit, one atom of carbon, one electron of hydrogen, or even one third of a quark. So. if a number say, .333...and one third, is multiplied by 3 to get 1.0, you are multiplying a 1/3 at the end of your number to get a whole number, but if you multiply .333... by three, it is not the same thing to start with, and will only equal .999... and not 1.0 because you dropped off the "one third part". 3 times one third will equal 1.0 because fractions are real. but 3 times .333... will never equal 1.0 because it is purely imaginary and leaves off the essential fraction.

"It is better to remain silent and be thought a fool, that to post a meaningless statement and remove all doubt." All numbers that are not exactly the same, such as 1 = 1.0, have an infinite amount of numbers between them. As for an average between 1.0 and .999... , consider that the average between 1.0 and .9 is .95 and between 1.0 and .99 is .995 and so between 1.0 and .999... is .999...5 nuff said.

Actually it does matter. You want to take an infinite like .999... and make it finite like 1.0 but when I do the same thing, like take an infinite universe and make it finite, 100%, you change the rules. (The decimal for 100% is 1.0). In the same way, you cannot multiply an infinite number such as .333... by any finite number such as 3 and conclude that it somehow equals some other infinite like .999... which would be like saying you could fly your spaceship to 33.3...% of the way to the end of universe, then do it again, and then do it a third time. Then you make the same mistake when you multiply .999... times finite 10. For sake of argument, what would you say is the answer to .999... times 2? or 3, or 4, or 5, or 6, or 7, or 8, or 9??? But, back to the point. 0.999... does not = 1. Learn it, live it, love it. And it seems like all of you on the other side seem to forget that in order for numbers to actually be different, there has to be another value in between. There is no other value between 0.999... and 1. Another false assumption. If you have an apple in one hand, and a kiwi in the other, and you bring them closer and closer to each other until you can't get another fruit between them, at what point are the the same fruit? If God comes into your heart, He is so close, the Devil can't get between, does that make you a God?

Sorry Doc, but Nmenth is absolutely right, and you are in error. This is simply because the human mind cannot perceive infinite. The universe is infinite. If you were to get into a spaceship and fly away from the Earth, when you are 99.999...% of the way to the end of the universe, would that be the same as actually arriving at the end? Yes, you could turn around , come back, and tell people you made it. Some would believe you, some would dispute you, some would not believe you. What would you show as proof? I'm sorry, but .999... did not, does not, and never will equal 1, any more than flying 99.999...% of the way to the edge of the universe is the same as flying all the way, 100%.