I’m trying to get to grips with what this term means. I’m interested in mysticism, philosophy etc and it seems like a fascinating idea especially considering the symbolism of the Aleph.
I have absolutely no maths knowledge… Just a GCSE in maths and some mental arithmetic.
Edit; thanks everyone for your useful responses!!
In: Mathematics
First, ask yourself, what is means “a number of something”. In the most naive way — you point your finger to every element of some set and say a natural number. So if you do that to every element exactly once and you counted to, say, five, you know there are five elements.
There are sets, that when you try to count, you will never stop counting. These are infinite sets. Like a set of all numbers.
But let us think more deeply about this concept of number of elements in a set — so if you count something, what you do is you create a function, a relationship between two sets. If two sets can be connected in a way that every element from one set is assigned one and only one element from the other and vice versa (this is called a bijection), then we say, that these sets have the same number of elements. A set that can be joined with this kind of relationship with a set of natural numbers from 1 to 5 is said to have five elements.
Along comes George Cantor, that tries to do this more formal approach with infinite sets. Cantor noted, that while we can create bijection between some infinite sets (e.g. you can show that there is the same number of natural numbers as there is of even natural numbers just by using the function that multiplies by two), you cannot create a bijection between natural numbers and real numbers. So he proved, that the number of elements in these two sets is different. He called the number of elements in the set of natural number aleph_0.
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