INTERVAL NOTATION and SET NOTATION >>>>>>&

[ramification]

I been aware of: Interval Notation and Set Notation...

...but really, :roll: they do the same thing, just presented in a different manner. What's the purpose for this. What's the pros and cons?

 

[stapel]

Interval notation is easy, but requires that the set of points be an interval. Since not all sets are intervals, or can even be expressed as such, other notation is necessary. Keep studying; with a few more years of mathematics courses, you may start getting into topics where you'll see the need for more than only one way of saying things.

Eliz.

 

[pka]

Ramification,
Maybe, I can give you a bit more of the background
In the foundation of mathematics we use formal languages.
(∀x)[x<4] is translated as “For all x, x is less than 4”. The use of two x’s is formal and not redundant.
A working mathematician would certainly use {x|x<4} or better the interval notation, (−∞,4).
But the formal definition for that set is (∀x)[x<4].

As to your further question about which notation to use, I will give you an example.
Most mathematicians use Q for the set of rationals, ‘q’ being the first letter of the word ‘quotient’.
We may want to consider the set of all rationals that are less than 4.
We could write that set as {x| xεQ ∧ x<4}
Or we could use interval notation: Q∩(−∞,4).