"There is an orange crow somewhere in the universe."

The above is a positive statement because it asserts that something exists. This statement can only be proven true; it cannot be proven false. To prove it true, all you have to do is locate an orange crow and your job is done. Proving that statement false is the same as proving its negative true. The negative of that statement is "There is no orange crow anywhere in the universe" or more simply "Orange crows do not exist." In order to prove that orange crows do not exist, you would have to search everywhere in the universe to make sure an orange crow wasn't hiding there. And even then, an orange crow might appear some place you've already searched so even if you've looked everywhere in the universe and failed to find an orange crow, that still wouldn't prove that orange crows don't exist. To prove it, you'd have to be aware of the contents of the entire universe all at once, and you'd have to somehow know for a fact that there aren't any orange crows in it. Clearly, an impossible task. This is where the notion "you can't prove a negative" comes from. Basically it states that it's impossible to prove the non-existence of something. Meaning, it's impossible to prove that something does not exist.

First let's prove a negative in the abstract world of mathematics and we'll move on from there. Let's consider the integers. An integer is an ordinary whole number like one (1) or negative five (-5) or seventy two (72). Does there exist a positive integer that is less than zero? Of course not, because the definition of "positive" excludes any number that is less than zero. It is impossible for a positive integer to be less than zero if we adhere to the definitions of "positive", "negative", and "zero".  Therefore, I can confidently state that positive integers less than zero do not exist.

Now let's move from the abstract world of mathematics to physical reality.  Let "Quiggle" be defined as follows:

Quiggle: (noun) 1. An intelligent life form that can find a positive integer that is less than zero.

While it is certainly possible that alien beings exist somewhere in the universe who are far superior to our intelligence and mathematical abilities, it's absolutely impossible for them to find a positive integer that is less than zero because by definition, such a number does not exist.  Since Quiggles are defined as beings who can find such impossible, non-existent numbers, it logically follows that Quiggles do not exist either.  It is impossible for a Quiggle to exist because a Quiggle is a being that can perform an impossible task. And look... I didn't have to search the entire universe to know for a fact that Quiggles do not exist. 

We can build an infinite regress of things that don't exist based on Quiggles. If a "Quigglatron" is defined as an electronic apparatus that can locate a Quiggle, then it logically follows that Quigglatrons do not exist either.  It is impossible to find an object or being that does not exist, so any device that supposedly can find non-existent objects or beings must itself be either a fraud or... non-existent.