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In this video, I wanna talk about sets of numbers
so, let's just dive in directly, shall we?
number 1: the natural numbers
Their symbol is N, and they're defined as '0,1,2,3...', well you get the point
But there's a catch: we can also define them as '1,2,3,..' and up.
And those 2 versions also have slightly different symbols.
Number two
The integers
The symbol of the integers is Z, and they're defined as the natural numbers but with all the negative components.
3: the rational numbers
Their symbol is ! and they're defined as p/q
with p being an integer, q being an integer, and q of course not equaling 0
4: the real numbers
Their symbol is R and they're defined as something special:
rational and beyond. But you might think, what's the beyond part in there?
Those are the numbers that you cannot represent by division of integers. Things like pi,
or squareroot of 2
Number 5: the complex numbers
Their symbol is C and they're defined as a+bi
with a being a real number, b also being a real number, and i^2 = -1
So now we're done
right?
Nope, we still got some more to go.
But, what can possibly be left?
The hypperreal numbers, the surreal numbers, the surcomplex numbers and
the hypercomplex numbers
but those are all topics for another video. To sum up,
we've got the natural numbers, the integers, the rational numbers, the real numbers
the complex numbers
and to also show you the new ones
the hyperreal numbers, the surreal numbers,
the surcomplex numbers and finally
the hypercomplex numbers