![]() ![]() To believe wrong concepts is a common condition of all people. Only when ignorance is willful is it something to be ashamed of. But, hey, I never claimed to be a mathemawhatsit. Hence I would argue that the difference of 0.000.1 between 0.999 and 1 is important in that respect, and that 0.999 is less than 1īut then, someone has probably already pointed this out, and the discussion suggested that they are some ignorant person who doesn't fully understand the intricacies of infinity, etc. Quote: Presumably people do not want this to be the case. does not have a last 9 for us to decrement to get 0.999.8. If you give me a proposed highest, I can always beat it by adding 1. But there is not a highest natural number. A last "9" would mean the same as a "highest natural number". has an infinite number of 9s - one nine in order for each of the natural numbers. has some "last 9" that we don't bother to write down. Quote: This process could then be repeated, eventually resulting in 0=1Īctually, this process cannot be carried out even once (unless you can come up with some sort of reasonable definition for your new notations - and even then, it is NOT going to be repeatable in such a way as to get to 0). By those standard definitions, both refer to the same real number. = 1, as these two notations already have definitions, which are not changed by defining additional ones. And even if you do define them, they have no bearing on the question of whether 0.999. If you want to talk about such "numbers", YOU have to define them first. The definition of decimal notation simply doesn't extend to these transinfinite decimal positions. Your whole argument simply ignores this problem, pretending that 0.000.1 exists! Let me try to be clear here: If you check the definition of decimal notation given above, you will see that it does not include such transinfinite decimals. As such, there is no such decimal notation as "0.000.1", for it would require an infinite number of 0s to occur before the 1. Quote: Note that in the notations above the 3 dots represents the digits repeating to infinity. If you will note in my post right above yours, I state (resulting in 0.999.8 ), then you still have 1. ![]() is the same as 1, then it presumably means that there can be no difference of 0.000.1. Medium (Moderators: towr, Eigenray, SMQ, william wu, Grimbal, Icarus, ThudnBlunder)īoldly going where even angels fear to tread. RIDDLES SITE WRITE MATH! Home Help Search Members Login Register ![]()
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