0 doesn't go into 1 at all, that's why we say it's 'undefined'. If 0 went into 1 X times where X is any well defined entity then 1/0 would be defined (as X). 

Division by zero (1 divided by 0) is undefined instead of being 0 because 0 can divide 1 infinitely many times. But that seems rather odd because the number 1 displays countable properties (ie. 1 glass of water, or 1 piece of toast) whereas 0 quantifies a count of null size. In other words, 0 cannot go into 1 infinitely many times when it hasn't gone into 1 at all. 

0 doesn't go into 1 at all, that's why we say it's 'undefined'. If 0 went into 1 X times where X is any well defined entity then 1/0 would be defined (as X). 

who actually cares 

Having interests? 

Here's an annoying maths thing someone told me. Xei will see right through it instantly obviously, but hey, it confused me a lot. 

Another version would be 1 = i*i = sqrt(1)*sqrt(1) = sqrt(1*1) = sqrt(1) = 1. 

Awesome... 

Last edited by Patrick; 03242012 at 10:36 PM.
Wow, I was about to start a thread on this general issue. It is really trippy. I have seen several variations, but this is the one I have been getting opinions on in the last few days. 

There is no contradiction. It is simply that the proof that sqrt(xy) = sqrt(x)sqrt(y) only works if x and y are nonnegative integers; it is not a general 'rule of math' for all entities x and y. Write out the proof and see. 

The proof you want me to check out involves imaginary numbers, so the proof involves an absurd premise. I know that a lot of the rules of math can be applied to imaginary numbers and the results are logical from the standpoint that there is such thing as the square root of 1. The premise is still absurd. You can use a lot of logical hypotheticals using Santa Claus also, but they are still based on an imaginary premise. 

No... the proof involves nonnegative reals. The point is that if they aren't, it doesn't have to go through: there is no requirement that the result should be true for complex numbers, and thus there is no contradiction: the issue is resolved. The same would apply to other things that you are presumably happy with, such as matrices; sqrt(A)sqrt(B) = sqrt(AB) doesn't hold for them either, and for the same reason. 

Last edited by Xei; 03242012 at 09:03 PM.
Jeez UM, you really hate complex numbers for no reason... 

It's an understandable mistake and one that was historically widespread... I believe British mathematics after Newton was quite hindered by it, much more progress was made on the continent where they were much faster to accept complex numbers for what they were. 

^ Yeah, that insight was very well explained. I'm actually doing a metaphysics paper on this right now. I'm also interested to see what physical phenomena or properties can be described by complex numbers and why. 

I must have misunderstood what proof you are talking about. Could you post it? Like I said, there can be a large amount of consistency in hypotheticals with absurd premises, though when taken to the nth degree, inconsistency can be shown somewhere. Movies about the paranormal don't have to have contradictions, for example, but they are based on absurd principles. The rule about multiplying square roots of negatives is such an inconsistency. 

To add a little to the original topic, zero is tricky because it has the property that for any x, 0 *x = 0. So dividing through by zero (pretend we're allowed to), we get x = 0/0. So we can divide zero into zero and get anything. 

Previously PhilosopherStoned
Isn't the premise that 1 exists made up too? 

Last edited by Wayfaerer; 03252012 at 12:29 AM.


That's another interesting way to look at it. I have always taught Xei's explanation, but I like your equation too. 

Xei, you should definitely become a professor. This is the first time someone has been trying to explain maths to me and I've actually understood it! 

I'm certain I'd be fairly miserable as a maths professor... I have been strongly considering doing part time private tuition though, especially for gifted kids who need some intellectual stimulation beyond the dismal mire of the UK curriculum. 

Last edited by Xei; 03252012 at 01:48 AM.
Didn't you get my pm a while back? I'm basically trying to find out how true new empiricism/psychologism is as the foundation of mathematics. Philosophy of mathematics  Wikipedia, the free encyclopedia 

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