# Which notation/abbreviation is appropriate to denote logical implication while writing proofs/solutions? [closed]

Find $$x$$ by solving the equation $$\frac{d (x^{2})}{dx} = 2$$

How should I write the remaining steps of the solution?

Should it be

$$\implies 2x = 2$$

$$\implies x= 1$$

OR

i.e. $$2x=2$$

i.e. $$x=1$$

OR

or $$2x=2$$

or $$x=1$$

OR

$$\therefore 2x=2$$

$$\therefore x=1$$

Which notations are appropriate?

• Your first one would be most normal in my opinion. The second one I have never seen. And the $\therefore$ is generally used for a "final important conclusion." I think it's technically correct for the third one, but very non-traditional. Feb 12 at 5:17
• Isn't the result $x=2$? Feb 12 at 5:56
• @PavanC. Okay, thanks. Feb 12 at 6:03
• You can leave out the symbols altogether —thus reducing visual clutter and improving readability— by simply writing (something like) "We can get to the answer via the following steps:". If individual steps might need later commentary or clarification, be sure to mark them with equation numbers (\tag{#} in TeX or MathJax). ... Of the given options, the first is best. (I tend to use "$\to$" instead of the heavier "$\implies$", and I'd add extra whitespace between symbol and equation.) The second and third are too much of a mix of words and symbols; the fourth is an overuse of "therefore".
– Blue
Feb 12 at 6:41
• It's worth noting the adage "Know your audience". Writing every step is important to guide unfamiliar readers (eg, students) through manipulations, or to highlight a particularly clever trick; it's also important if there may be a mistake that needs to be detected. But, if your audience knows Calculus, then walking through basic algebraic steps wastes their time; just write "and so $x=1$". If there's a bit of work involved: "one can show that $x=1$". Indeed, authors often skip-over even non-trivial arguments with the somewhat cliché "showing this is left as an exercise to the reader". :)
– Blue
Feb 12 at 7:06