That's only true if changing the numerical base retains the quality of the value. Try dividing 1 by 3 in a base 3 system, you'll find the endless digits don't occur. It makes a solid integer instead, like so; (left column is base 3, right column is base 10) 1/10 = 0.1 1/3 = 0.333' 0.1*10 = 1 0.333' * 3 = 1 The 0.999' = 1 only is true when the 0.999' actually represents a 1/3rd * 3 And thus the 0.999' = 1 only if it is representing the 1/3*3 If you are referring to the real 0.999' which also exists but is not equal to 1/3rd * 3, then no it does not equal 1. It's existence as 0.999' = 1/3*3 = 1 only occurs as a result of a quirk of the decimal numbering system, which is simply an artificial system used to express the underlying geometry of existence. So in short, there are two 0.999' symbols one which represents the real value 0.999' which does not equal 1. And there is the 0.999' which actually represents 1 but is generated as a numeric symbol for 1/3*3 as a quirk of decimal. This is one reason Pi is so interesting cause it doesn't matter what number base you use it still generates an endless chain of non-repeating digits. But I'm a philosopher not a mathematician, but I can still tell the difference between the symbol 0.999' and the actual number 0.999' which are two different things. Go watch Numberphile they cover various mathematical concepts, they might have a video on it. If I seem a bit discoherent it is cause I recently passed the 24 hours awake point. So I am going to bed, goodnight internet.