Quid quid latine dictum sit, altum videtur.
Anything stated in Latin seems profound.
No commas should follow any of the following Latin abbreviations, with only two exceptions ("i.e." and "e.g.") that must be followed by a comma.
Medical abbreviations | Tironian notes by Tiro (slave/feerman of Cicero)
Yes, but the word "respectively" and the symbol "resp." have different syntaxes. The latter should probably be used exclusively in a mathematical context. It's not a general-purpose abbreviation of the former...
In her blog today (2006年11月18日) Margaret Marks was kind enough to quote my two-line definition of signed infinities as an actual example of the mathematical use of "resp.". (I just noticed this when someone triggered her link to <Numericana>.)
A (contrived) example would be: "The square of 2 (resp. 3) is 4 (resp. 9)."
That could also be stated: "The squares of 2 and 3 are 4 and 9 respectively."
The two syntaxes are different, as advertised. Occasionally, the former syntax can be more convenient and mathematicians find it easier to parse.
It's not a bad thing to have a few keywords which allow the reader to recognize an English sentence as a mathematical statement, because that may deeply affect the meaning... The most critical feature is undoubtedly that mathematical discourse (expressed in any "natural language") is inclusive "by default" whereas everyday speech is not. To a mathematician, the statement "a circle is an oval" is clearly true. It would seem nonsensical to people accustomed to a common "exclusive" definition stating, at the very outset, that an oval is a non-circular shape...
By comparison, the use of "resp." (which puzzled Margaret) is a minor issue ! However, this and other mildly jargonistic terms may actually be helpful in warning the reader that a sentence is meant to be a mathematical one (which is to be interpreted as inclusively as possible, even if only "common" words are used). Such clues help build what linguists call a "context". Mathematical texts may acquire strange meanings when an attempt is made to read them "out of context".
Separators are common in a financial context, but they are rarely used within scientific equations, where they would decrease readability rather than improve it.
Also, there are cultural differences for separators (dots or commas). In English, the comma is used to separate 3-digit groups, whereas a period is used for the "decimal point". In French it's the exact opposite. A Frenchman who's otherwise fluent in English could easily misinterpret 999,998 to mean 999.998.
The 22nd CGPM (October 2003) reaffirmed Resolution 7 of the 9th CGPM (1948) by ruling that both the comma and the dot were allowed as decimal markers. Therefore, neither is acceptable in an international context as a typographical separator between groups of digits. The international convention is to use some spacing between 3-digit slices. If at all possible, such spacing should be thinner than the regular spacing between words.
Unless their rough magnitude is clear from the context, it's a good idea to avoid decimal numbers featuring exactly 3 digits after the decimal marker and 3 digits or less before it (except in the unambiguous case of a single leading zero digit). Many people could otherwise misinterpret such numbers by a factor of one thousand.
When separators are used, the need for an unsightly single-digit "group" is normally avoided by allowing the leading group to include up to 4 digits. In particular, separators are not used for integers up to 9999.
Number theorists who deal routinely with large integers never use any separation between groups of digits (separators or spacing) because very large integers are unreadable anyway. In this digital age, a marginal improvement in readability is less important than the ability to cut and paste such long numbers uniformly.
Non-blank separators are never used to the right of the decimal marker. Spacing between decimals is best restricted to the (rare) tabular display of many decimals for a specific mathematical constant (in which case groups of 5 or 10 decimals may be more typical than groups of 3). The ISO 31-0 standard says:
" To facilitate the reading of numbers with many digits, these may be separated into suitable groups, preferably of three, counting from the decimal sign towards the left and the right. The groups should be separated by a small space, and never by a comma or a point, nor by any other means. "
For example, [0,1] is the set of all real numbers between 0 and 1, both extremities included, whereas ]0,1] is the set of all nonzero such numbers.
We do not recommend a notation with ordinary parentheses for excluded extremities; namely (0,1] in the latter example above. It's unfortunately dominant in "domestic" English texts (it puzzles international audiences).
The chief reason why the "domestic" notation is unacceptable is that (0,1) is universally accepted as denoting an ordered pair (an element of a cartesian product) in any modern context. Using that same notation to denote ]0,1[ is confusing at best, for any audience.
The year is listed first as a 4-digit number. Dashes are used, not slashes.
Taken together, those two clues properly indicate that the date identification uses the international ISO 8601 standard in its simplest form...
That standard specifies that the most significant numbers must be listed first, as is the case with digits in ordinary decimal numeration (thus, the month follows the year and the day of the month is listed in third position). Months and days are always given as two-digit numbers, with a leading zero if necessary. This design makes lexical and chronological orders coincide, as is most desirable.
This is simple and logical enough when it comes to identify a specific day.
Unfortunately, the standard also allows other formats for dates and times which cannot be assumed to be self-explanatory. We think these are best ignored outside of specialized contexts For example, separating dashes may be dropped, time can be included and a week number could be specified instead of a month number... Such add-ons to the above basics only hinder general acceptance.
In digital contexts, ISO 8601 dates of the above type are sometimes followed by separate (nonstandard) time stamps.
Such customary time stamps feature a column character ":" between hours and minutes, from 00:00 to 23:59. This is reminiscent of the ubiquitous displays for digital 24-hour clocks, which need no introduction. The only "unusual" part of the convention is a leading zero for the hours before 10am.
For added precision, another ":" may be added, followed by a two-digit number of seconds, from 00 to 59. For the ultimate in precision, this number of seconds may be given with as many decimals as needed (using a decimal point).
Basic ISO 8601 dates followed by such time stamps (with a single blank space inbetween) identify a precise time. By design, the lexicographical ordering of such identifications is the correct chronological order (whether the time stamps are given at the same level of precision or not). Examples:
2006年10月31日 23:45 2006年11月01日 04:05 2006年11月01日 04:05:10 2006年11月01日 04:05:10.3 2006年11月01日 04:05:10.32346159 2006年11月01日 04:06 2006年11月01日 05:00
With thanks to Steve Healey ("BonusSpin") of Edison, NJ, a math & physics junior at Rutgers (New Brunswick, NJ) who appeared on the ABC TV show "Who Wants to Be a Millionaire?" on Sept. 14 & 17, 2000.
Thanks also to Keith McClary for suggesting (2004年05月24日) multiplier and multiplicand, especially for noncommutative multiplications.
Note the consistent use of the suffixes, which are of Latin origin:
In high-school parlance, the negative integer "-7" is pronounced "negative seven". Outside of the classroom, almost everybody says: "minus 7".
The number 0.7 (namely seven tenth or 70% of a whole) is also written .7 and pronounced either "decimal seven" or "zero point seven" (the latter being preferred in modern "straight talk").
Here are the basics:
If A and B are strings, I call their concatenation "A before B".
There's also the issue of indicating parentheses and groupings when pronouncing expressions. If the expression is simple enough, a parenthesis is adequately pronounced by marking a short pause. For example, x (y+z) / t could be spoken out "x times ... y plus z ... over t" (pronouncing "y plus z" very quickly).
The locution "outside of" can also be used to introduce an opening parenthesis, matching a closing parenthesis corresponding to a short pause.
When dictating more complex expressions involving parentheses, it's best to say open parent' and close parent' as needed.
From a semantical viewpoint, the meaning of complex arithmetical expressions involving elementary operators is the value obtained by applying the operators in their conventional order of precedence. Unfortunately, English-speaking schoolchildren are often taught to associate this with the mnemonic sentence "Please Excuse My Dear Aunt Sally": Parentheses first, then Exponentiations, Multiplications, Divisions, Additions and Subtractions... This should not be relied upon, for the following reasons:
Use parentheses to make sure you're understood!
To improve readibility, other styles of so-called grouping symbols are available besides ordinary parentheses. In a valid expression, these are always used in matching pairs enclosing a valid expression:
The above issue arises for physical units, especially when an electronic calculator is involved.
For example, the SI unit for entropy or thermal capacity is the joule per kelvin (J/K). A specific thermal capacity is a thermal capacity per unit of mass, so the SI unit is the joule per kelvin per kilogram or J/K/kg. It's a bad idea to write that down as J/K.kg (joule per kelvin-kilogram) because of the above ambiguity, although most professionals won't even blink. A modern trend (which I dislike) is to forgo the use of the division sign (the solidus) entirely when expressing physical units. According to this relatively new fashion, the abbreviation for the previous unit would be:
J . K-1 . kg-1 = m2 . s-2 . K-1
I still favor parsimony and prefer to express gravitational fields in N/kg (newtons per kilogram) rather than in m/s/s , m/s2 or m.s-2