Why are there five notations when all you need is two(greater than and less than)?.  I think you don't need the does not equal one because saying greater than or less than makes it not equal.o

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Notation makes it easier to talk about certain things without having to write a lot.  In some functions, you'll want to be able to use not equal to, or ≠, to be able to say that x can be everything but a certain value, perhaps zero. For example, y = 1/x, x ≠ 0  (because we cannot divide by zero).Also, it is often convenient to use ≤, and ≥ in order to include a number.  For example, we cannot take the square root of a negative number, so if we have the function y = sqrt(x), we want to specify x ≥ 0, because it can be equal to 0, but not less than. Notation is a matter of convenience, we don't want to write out, x greater than or equal to 0 in all our mathematical problems.