Colon in math equations
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Both of these types of equations are used consistently in a project I am working on. I am trying to understand the difference between the two as to when to put the space after the colon and when not to. Is it a safe assumption that the colon is being used as "such as" when it is enclosed in some type of grouping symbol?
f: A > B which is considered mapping with no space before or after the colon
{x ϵ Q : < x < 2} where the colon is "such as" with no space before and a space after
I also have the symbol := used frequently, example inf E := b, so is the colon attached to the E or equal sign and where is the spacing?
Another concern I have in this project is the usage of the double-struck letters on various letters. I am following the rule 7.10 in Nemeth to use the script typeform and added the TN. But I also have a very fancy script P in print referring to the power set, so how do I make this difference? I have thought of putting a TN on the TN page stating that the script is omitted on the P when referring to power set but concerned I will have other references to a P that is not a power set.
For the f: A → 𝒫(A), you might have already found the "function notation" question in this forum, which touches on the seven different mathematical uses for colons. I agree with your assessment that this is giving a name to a map, as defined by WolframMathWorld. As you said, in braille such a colon (for mapping) would be transcribed unspaced, and it would need a punctuation indicator.
For something like {x ∈ ℚ : x² < 2}, I agree with your assessment that the colon here means "such that." So, the expression {x ∈ ℚ : x² < 2} says, "x is an element of the set Q such that x-squared is less than 2." The "Colon and letters in sets of numbers" question in this forum talks about this "such that" role for a colon and recommends transcribing it unspaced (no blank braille cell before or after the colon meaning "such that").
Since we recommend transcribing both the mapping and "such that" colons completely unspaced, it may not be necessary for you to completely understand the difference between the two. For what it is worth, I agree with you that a "such that" colon is likely to be part of an expression within grouping symbols (most often curly braces). I would also suggest that a "such that" colon will have the same variable both before it and after it, like the x in our example expression above.
The print sign := (a colon followed by an equals sign) seems to mean "is defined as" (I first found this definition in a thread on StackExchange). How are you thinking about transcribing the := sign?
Regarding your concern about double-struck letters and the script P, what if you used the Nemeth Code script type form for the P's meaning "power set" and another Nemeth Code type form (italic, bold, or sanserif) for the letters that are double struck?
–Kyle
My thought for the colon followed by an equal sign is putting these two symbols together without a space. The attached document shows the explanation from the text. I had wondered about putting the dot 5 between them to show they are horizontally.
I agree with you on the double-struck letters and will check through the book on that idea to see what is the best font to change to.
Clarify for me the spacing for the colon used as "such that". An Introduction to Braille Mathematics Using Nemeth Code within UEB Contexts 6.7.16a states that a space would follow the colon in braille when used as "such that". I have looked to see if there is an update to remove the space following but I cannot find one.
Connie,
I got both ahead of and behind the times.
In the updated Nemeth Code, which is currently neither approved nor published, it will say that since the colon meaning "such that" is still a colon–a mark of punctuation–we should treat it as such and use a punctuation indicator before it (unspaced from the material it follows), and space after it.
The only currently approved and published rule reference we have is example (9) in §27.f [on print page 34] of the 1972 Nemeth Code, which shows a colon that means "such that," and the colon is totally unspaced. I always try to recommend following the currently approved and published rule.
It will be soooo exciting when the updated Nemeth Code is published!
–Kyle
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