mathematical logical symbol
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.
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If you are trying to insert the therefore symbol into a Word document
Hold down the ALT key and type 8756
In Excel, select insert, then select Symbol.
Then using the pulldown menu by Font, select Symbol
Type character code 92 in decimal.
You can do the same in Word as well.
in the symbol section there fore sign was not there but thanks for ALT+8756 was useful in word and than copy and paste to Excel
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: $$P=o(Q) \ \Longleftrightarrow\ \deg P<\deg Q\, .$$