Does 0 = Infinity?

[Alex K]

Hi, all. 

This is something which I'd considered a while ago. My logic is a little shaky but my proposition doesn't appear to be too full of holes. 

I guess the principle belief that 0 = infinity would assume that values exist as absolutes. If we were to say that nothing exists, there would be an endless stream of nothing. This was practically the core belief (and, more to the point, revelation) when I was considering this principle for the first time. 

I really don't think my assumption functions in mathematical environments that do not assume absolutes, rather they function as relativistic. In other words, if you have none of something, that doesn't suddenly form a singularity in the space where that something would inhabit. 


My point is that, if we were to create a closed environment involving only a single inhabiting factor, if said factor did not exist (and assuming that this system was an undefined size, eg. the universe), would that not create a space infinitely large? If borders had a value of zero, would they not cease to exist and thus render a potentially infinite empty space? 


I think the reason that this is a difficult problem for me (and maybe for most people, too) is that 0 and infinity are both practically irrational. I believe that the principle of 0 was originally suggested by an Arabic mathematician, but I personally think that it does not infer mathematical properties, rather more philosophical. If we were to hypothetically state that 0 does unarguably equal infinity, it would point towards my two beliefs that, 1. it is not strictly mathematical, 2. it is irrational and thus would not strictly have any place in rational mathematical works (though perhaps hypothetical mathematics). 

Alas, 0 exists as a placeholder for the lack of any element (and of course as a suffix for factors of ten). I see why it is still relevant even today. I suppose my attempts to rationalise it by, ironically, quantifying it with an irrational value is simply my way of showing that it is more complex of a value than we may originally think back in primary, secondary, or even college. 


That's my rant over, at any rate. I'd love to hear everyone else's opinions on the matter.

Almost nothing you say about 0 as a number is true. The first half of your text even seems like complete gibberish. I don't know what you talk about with nothingness and infinite space. What does any of this have to do with the number 0?

0 is an element of the rational numbers, not irrational in the sense mathematicians use the word, it is not a placeholder but an ordinary element of the rational and real numbers. It does have an effect, e.g. in multiplication, 6*0 !=6. The only unusual property it has in the field of real numbers is that division by it is not defined.