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Talk:Arithmetic progressions
<math>n</math>
Please read Template talk:Selected Recent Additions#<math>n</math> for why I keep adding \scriptstyle
and the \,
(comma space Latex command) hack to always force (by the use of a LaTeX command) the rendering of LaTeX into PNGs for consistent apperance of mathematical variables and/or equations. — Daniel Forgues 08:20, 6 August 2012 (UTC)
Compare
'''Arithmetic progressions''' are [[sequences]] of the form <math>a(n) = mn + c</math>, where <math>m</math> and <math>c</math> are constant, therefore <math>a(n) - a(n - 1) = m</math> and <math>a(n) \equiv c \mod m</math>. For example, 4, 16, 28, 40, 52, 64, 76, 88, 100, 112, ... (A017569) is an arithmetic progression with <math>m = 12</math> and <math>c = 4</math>. In terms of [[growth of sequences]], nonconstant arithmetic progressions have linear growth.
giving
Arithmetic progressions are sequences of the form , where and are constant, therefore and . For example, 4, 16, 28, 40, 52, 64, 76, 88, 100, 112, ... (A017569) is an arithmetic progression with and . In terms of growth of sequences, nonconstant arithmetic progressions have linear growth.
with
'''Arithmetic progressions''' are [[sequences]] of the form <math>\scriptstyle a(n) \,=\, mn + c \,</math>, where <math>\scriptstyle m \,</math> and <math>\scriptstyle c \,</math> are constants, therefore <math>\scriptstyle a(n) - a(n - 1) \,=\, m \,</math> and <math>\scriptstyle a(n) \,\equiv\, c \pmod m \,</math>. For example, {4, 16, 28, 40, 52, 64, 76, 88, 100, 112, ...} (A017569) is an arithmetic progression with <math>\scriptstyle m \,=\, 12 \,</math> and <math>\scriptstyle c \,=\, 4 \,</math>. In terms of [[growth of sequences]], nonconstant arithmetic progressions have linear growth.
giving
Arithmetic progressions are sequences of the form , where and are constants, therefore and . For example, {4, 16, 28, 40, 52, 64, 76, 88, 100, 112, ...} (A017569) is an arithmetic progression with and . In terms of growth of sequences, nonconstant arithmetic progressions have linear growth.
Although it is quite tedious (and clutters the code) to add all those \scriptstyle
and \,
all over, the result looks much sleeker, don't you agree? — Daniel Forgues 08:32, 6 August 2012 (UTC)
- I agree. But I haven't learnt the subtleties of
\scriptstyle
and \,
, so sometimes if it's not convenient for me to copy and paste one of those you've already done with those I'll just dispense with them and leave it to you to add them when you get around to it. I hope you don't think this a burden or an imposition. Alonso del Arte 02:25, 7 August 2012 (UTC)
- Actually the \scriptstyle looks considerably worse on my screen. Neither lines up with the text and neither is the same size (scriptstyle smaller, the other bigger). Worse, the smaller \scriptstyle is actually aligned *below* the normal text, making it seem yet smaller.
- Ideally the choice would be made by individual users in their preferences, but unfortunately those are insufficiently fine-grained. Charles R Greathouse IV 03:05, 7 August 2012 (UTC)
- From now on, should I continue adding those
\scriptstyle
and \,
to get like the second example or should I leave things alone to get like the first example?
- From now on, should I continue adding those
- Note that if we ever use MathJax, I suspect (not sure though... it might depend on the behavior/configuration of MathJax, some testing would be required...) that adding
\scriptstyle
and \,
might turn out to be better... but then we don't yet whether or not we will ever use (or test for suitability...) MathJax. — Daniel Forgues 08:24, 7 August 2012 (UTC)
- Note that if we ever use MathJax, I suspect (not sure though... it might depend on the behavior/configuration of MathJax, some testing would be required...) that adding
- Insofar as the purpose of \, is to override the user's preferences, I would say that it should not be used. This becomes more important if MathJax is enabled, because a person who {likes|dislikes} MathJax should be able to {force|bar} its use through preferences, regardless of defaults.
- \scriptstyle has its uses: it's designed for inline formulas, $...$ rather than $$...$$ or \[...\]. I wish it were never used because it looks terrible on both computers I typically use. But if other people like it I suppose it's fine. But it should only ever be used for inline formulas. If you write
:<math>...</math>
on its own line, it should certainly not use \scriptstyle. - Charles R Greathouse IV 16:07, 7 August 2012 (UTC)
- If you write
:<math>...</math>
on its own line, it should be\displaystyle
(which is the default only when LaTeX is rendered into PNG). For example
- If you write
<math>a(n) = n^2</math>
yields (not rendered into PNG)
<math>\displaystyle a(n) = n^2</math>
yields (rendered into PNG)
- while
<math>a(n) = n^2 \sqrt{n}</math>
yields (rendered into PNG)
- while
- and with the
\,
hack,<math>a(n) = n^2 \,</math>
yields (rendered into PNG)
- and with the
- which makes the display style consistent. — Daniel Forgues 08:52, 9 August 2012 (UTC)