mathematical logical symbol
The inverted form of the therefore sign ( 
) used in proofs before logical consequences, is known as the because sign ( 
) and it is used in proofs before reasoning.
This symbol just means 'because'. If it was facing up, it means 'therefore'.
Kinda feel like this is too short but I guess there's not much to this question.
Is there any better alternative to the three-dot notation?
The usual general advice is to use words instead of symbols.
The best notation is no notation; whenever it is possible to avoid the use of a complicated alphabetic apparatus, avoid it. A good attitude to the preparation of written mathematical exposition is to pretend that it is spoken. Pretend that you are explaining the subject to a friend on a long walk in the woods, with no paper available; fall back on symbolism only when it is really necessary.
(Paul Halmos, How to Write Mathematics, p. 40.)
This applies particularly to the three-dot notation.
Do not misuse the implication operator ⇒ or the symbol ∴. The former is employed only in symbolic sentences; the latter is not used in higher mathematics.
Bad: a is an integer ⇒ a is a rational number.
Good: If a is an integer, then a is a rational number.
Bad: ⇒ x = 3.
Bad: ∴ x = 3.
Good: hence x = 3.
Good: and therefore x = 3.Bad Theorem. n odd ⇒ 8|n² − 1.
Bad proof.
n odd ⇒ ∃j ∈ Z, n = 2j + 1;
∴ n² − 1 = 4j(j + 1);
∀j ∈ Z, 2 | j(j + 1) ⇒ 8 | n² − 1This is a clumsy attempt to achieve conciseness via an entirely symbolic exposition.Combining words and symbols and adding some short explanations will improve readability and style.
(Franco Vivaldi, Mathematical Writing, p. 4 and 132.)
The context isn't entirely clear so I'll assume this is about teaching. Then, I support Pedro's answer but also want to add that doing both verbal and symbolic versions may be a good idea. For example:
Theorem. A polynomial has a higher order than another if and only if its degree is higher.
In other words, for any two polynomials 
and 
, we have:
