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Title: The concept of infinity
Description: These notes brake down the complete concept of infinity and it will show you how you can count past infinity
Description: These notes brake down the complete concept of infinity and it will show you how you can count past infinity
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different subsets you can make from it” and that’s actually really true
...
The formula for the power set is
2^N where N is how many members the original set has, in this case 3
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To figure out if this set is a bigger infinity than aleph-null you need to keep
producing new subsets that are clearly not listed anywhere on the aleph-null sized list, because
than we will know that we’ve got a set with more members than there are natural numbers
...
So the power set of the naturals will always resist a bijection
with the naturals, so it’s an infinity bigger than aleph-null
...
And that would guarantee that aleph-null exists
...
This assumption states that if you take a set like the set of all natural
numbers and replace each element by something else the thing you are left with is also a set
...
You
will get omega plus one until omega plus omega, which can be replaced by omega times two
...
Using this principle you can achieve omega squared
...
And that is called epsilon-nought
...
In this case that ordinal is called omega
one, not omega plus one, omega one
...
The cardinal number describing the amount of things used to make an arrangement with
order type omega one is aleph-one
...
We won’t get an answer yet but in the mean
time we can go even higher and higher using the scheme of replacement
...
We can reach bigger and bigger infinities each time and
wherever you land there will be a place of even bigger numbers allowing you to make even bigger
jumps than before
...
Lets take all of this in mind and focus on the following, we have been using these numbers like
there’s no problem with them but if (at any point down the line of natural numbers) you can always
add one, can we really talk about this endless process as a totality and then follow it with
something
...
We are not dealing with science, we are dealing with math
...
With axioms it’s true because we
say it is
...
Mathematicians create
a universe themselves
...
If you just read this entire piece and still refuse to accept it that’s okay, because that makes
you a finitist, but if you accept it (like most mathematicians do) you can go very far
...
That is true because people
with that mind set of accepting that there might be something beyond public believes can achieve
far greater than those who can’t, just because they accept that things are
Title: The concept of infinity
Description: These notes brake down the complete concept of infinity and it will show you how you can count past infinity
Description: These notes brake down the complete concept of infinity and it will show you how you can count past infinity