mathematical logical symbol
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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.
Type 2235 and press Alt+X. This will insert the symbol in MS Mincho, which is perhaps not the best choice. If character 2235 is not included in the font you're using, you might prefer to insert it from Arial Unicode MS, using the Insert | Symbol dialog.
Thanks, Suzanne! It works like a charm. I read about alt+x elsewhere but could not make it work. The choice of fonts as you noted made the difference. Thanks.
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 $P$ and $Q$, we have: $$P=o(Q) \ \Longleftrightarrow\ \deg P<\deg Q\, .$$