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July 10th, 2019, 09:47 AM  #1 
Senior Member Joined: Oct 2015 From: Greece Posts: 139 Thanks: 8  May undefined values will eventually be defined?
So we know that division by zero is undefined, a lot of limiting values are also undefined. Does that mean that we will never find an answer to these questions? For example $\displaystyle \sqrt{1}$ was also undefined but we defined it. Does this mean that there is hope that someone will eventually for example find a solution and define $\displaystyle \frac{a}{0}$? where a constant real number. Or do we know somehow for sure that this will never be defined no matter what? Last edited by babaliaris; July 10th, 2019 at 09:49 AM. 
July 10th, 2019, 03:44 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,631 Thanks: 1470 
I think you have a bit of a skewed vision about mathematics. Things like $\sqrt{1}=i$ would exist and be just as valid if mankind never existed. It's not a matter of mankind defining these things. We define the labels that we use for them, that's all. Over in Andromeda they use some other symbol for $\sqrt{1}$ but it's the same entity. The problem with something like $\dfrac a 0$ is that it results in entities that aren't unique. If $\dfrac a 0 = Q$ then $Q\cdot 0 = a$ But $Q \cdot 0 = 0, \forall Q$ so the whole thing breaks down. The spherical representation of the complex numbers does have a sort of infinity to it, but even so, division by zero is an undefined operation. This all is just hand wavy enough to cause the real mathematicians to show up in a huff and perhaps give some more rigorous treatment of what I'm trying to describe. Last edited by skipjack; July 10th, 2019 at 05:19 PM. 

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