So I got curious today about the concept of infinity.
According to any evidence, basically, the space is an infinite entity, and that the galaxy continues to expand into nowhere, demonstrating that there is so much more to be explored.
Yet, such a human concept of Internet which is measured by more than terabytes now is also infinite, yet is existing in our laptops. So the so called cyber-space and the immeasurable infinity of space and time and the conflict about the competition of the superiority creates a natural conundrum of what is bigger?
It is hard to see what is bigger because either are expanding, and the second one is the product of a human mind which is already endless. Just an interesting question which I could not find an answer to so I decided to call up you guys (Armor Squad XD)
Now, I can keep doing that for infinity because all numbers increase to a true infinity ... If there were some theoretical end to whole numbers beyond human measurement you'd run out of even numbers
As Fish pointed out, this is a contradiction. The stipulation here is that the set of whole numbers is an infinite set. This implies that the set of even numbers (as well as odd numbers) is also an infinite set.
You're reaction to this is completely understandable. It's entirely unintuitive that the set of even numbers should be the same size as the set of whole numbers. From what I understand, most of the mathematicians in Cantor's time thought this idea was ridiculous. I've seen papers that actually run the proof backwards. The thought is that, if a theory produces some crazy, irrational result, then some premise or axiom of the theory is wrong. So mathematicians would work backwards to try to find this flawed premise.
there is still the distinct central point at which -1 transfers to 0 which transfers to 1. This series of two odd numbers with no even numbers in between creates a difference between the relative sizes of the infinities for odd and even numbers
The requirement of being an even number is being divisible by 2 with no remainder.
As it turns out, everything that is a multiple of 2 is also divisible by 2. But even by that definition, 0 is an even number since 0/2 = 2.
0 itself is a visual representation of nothingness, the antithesis of infinity.
The strange properties you list that 0 has can be explained both mathematically and intuitively (one really, really weird property 0 has is as an exponent, e.g. 5^0 = 1). But one thing it does do is behave exactly as you'd expect an even number to behave. For example, two even numbers added together gets you an even number. And sure enough, (even) + 0 = (even).
But more to the point, '0' is a numeral, which is a visual representation of a number. I think you're conflating the mathematical concept of 0 with the concept of nothingness. There is a sense in which zero is nothing, however. We can recursively define the even whole numbers, starting with 0. In this case, zero would be the empty set - the set of all things not identical to themselves. It would contain no elements. But this is a different concept from nothingness, which isn't a mathematical one.
You're reaction to this is completely understandable. It's entirely unintuitive that the set of even numbers should be the same size as the set of whole numbers.
Yes, there are many things that are unintuitive with anything approaching infinity like (infinity)/0 = (infinity)
0/2 = 2
A minor mistake there, 0/2 = 0 But absolutely right nevertheless. Thanks!
5^0 = 1
That's not weird at all. It is just rarely explained. People always know that 1+1 = 2 but find it very difficult to think that 2=1+1. It is the way we've gotten used to thinking. Using the same reasoning, we may know that 5-5=0 but it is difficult to think that 0=5-5 (0 could be equal to an infinite amount of things)
So what we really do when we have the 5^0 is 5^(5-5) which is 5^5/5^5 = 1. It is just that we learn to do it instantly. We don't have to replace 0 with 5-5, any numbers would do but exactly because it doesn't matter, we do it instantly without actually replacing the numbers.
The internet as we know it, is a technological construct that exists within the confines of human-occupied space. There is far more observable space than occupied space, so we can observe more space that is devoid of internet then space where the internet does exist. Therefore space is bigger then the internet.
Depends on physical matter or data.Space is basically the lack of matter and it's constantly growing so it's bigger size-wise.The internet,however,is also continually growing in data so it's larger in that way.Correct me if I’m wrong.
