question, what do you call something that seems to go on and on without ever getting to the end? infinite.. good answer, now lets say you have something that seems to go on and on, but you knwo there is an end, but it just cant be reached, you would also call the infinite... so there are two types of infinite, we all agree. let us continue.
now lets say you became the head accountant for the cosmos and are in charge of counting up all the accounts of the universe and beyond.
there is the number 3, and 1/3 is 3 repeating to inifinite, we will say the infinite we are talking about is the one with no end at all. next we say 2 X 1/3, or 2/3.. this si all 6's repeating to the same infinite, never ending. now 3 X 1/3 or 3/3 is 1?, or 1.0 in the other view we can say since 1/3 is all 3's, and 3x3 is 9, then 3/3 is actually .999 repeating, and never quite 1. now as head accountant, your superior has asked you to mend this discrepency, since both answers are not exactly equal. ( yes i know people say they are the same .9999 and 1, but lets put this aside for a moment please)
i once held this fake position and here is my answer. if by 1/3 u mean 1/3.00000000000 and zeroes to inifinite, the one with no end at all, i can not solve.
If you mean that it is 1/3.00000 but you know there is a last zero, but it is completely unattainable 9 the second version of inifinite we discussed beforehand)i can solve to a degree. Now let us use our mind and transport to the last digit place, and we will place the number 3, so in fact it is 1/3.000000 infinite0003 get it? long string of zeroes and a three in last place. then the answer will still be .3333 since the last 3 wil just be another 3 at the end of the long set of infinite 3's.. right?? take a few minutes to gather your senses, but you will realize this, it just another 3 of smaller value. now 3 x 1/3 or .3333 X 3, is .999 inifinite (neverending). now if u have 3/3.000000inifinite 3, then you have a true defnition of .9999 never ending. what i am trying to say here is this. there are two types of infinite, and all the repeating same numbers that seem to go on and on, in a sense continue without end, but if you are attempting to make the fraction whole again ie change 1/3 into 3/3, you must realize the last number that should be there is infact not a zero, but another number.. what do you guys think i have a very in depth analysis of this but only wish to discuss it with people are are actually interested inthis