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It specifies where it would be OK to add a line-break where a word is too long, or it is perceived that the browser will break a line at the wrong place. Whether the line actually breaks is then left up to the browser. The break will look like a space - see soft hyphen below when it would be more appropriate to break the word or line using a ...
This is not a problem with a block displayed formula, and also typically not with inline formulas that exceed the normal line height marginally (for example formulas with subscripts and superscripts). The use of LaTeX in a piped link or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to ...
A summary provides an overview of the data of a table for text and audio browsers, and does not normally display in graphical browsers. The summary (also a high Manual of Style priority for tables) is a synopsis of content, and does not repeat the caption text; think of it as analogous to an image's alt description.
The <math> tag is best for the complex formula on its own line in an image format. If you use this tag to put a formula in the line with text, put it in the {} template. The {} template uses HTML, and will size-match a serif font, and will also prevent line-wrap.
A non-paragraph line break, which is a soft return, is inserted using ⇧ Shift+↵ Enter or via the menus, and is provided for cases when the text should start on a new line but none of the other side effects of starting a new paragraph are desired. In text-oriented markup languages, a soft return is typically offered as a markup tag.
This help document doesn't address the addition of trailing and leading line breaks when transcluding page text using Standard section transclusion. Per Help:Transclusion#Standard section transclusion : This method may sometimes introduce a leading or trailing line break or newline, depending on the markup in the source and target pages.
Strikethrough}} draws a line through the text provided in the first unnamed parameter. The template embeds the parameter in an HTML <s>...</s> element, producing output such as: this, i.e. text with a line drawn through its middle. Outside articles, it can be used to mark something as no longer accurate or relevant without removing it from view.
The TeX markup of <math>...</math> uses a serif font to display a formula (whether as SVG or HTML). HTML math expressions should use the {} template so they display in a serif font as well. Doing so will also ensure that the text within a formula will not line-wrap, and that the font size will closely match the surrounding text in any skin.