In English, one reads “5x ≥ 2y” aloud as:
Five ex is greater than or equal to two wye.
The is and or make the sentence literally true by the conventions of ordinary English.
It is quite a mouthful to say. Occasionally I hear people say “greater than equal” to hurry, omitting “is”, “or”, and “to”, but holding “than” a little long to give equal time to each of the three words. More commonly, though, people just get very good at saying “is greater than or equal to” very quickly.
The closest way I know of is to say one number is "over" another. For example:
- "Three-hundred thirty-four over eleven" for 334/11
But that doesn't seem quite right to me, because one number being "over" another isn't really what makes a fraction, since that's notation.
But you're "reading aloud" notation, so it's not really clear to me why this troubles you. I wonder if you have a similar problem, for example, with saying "period" to mean - that's final. Do you ever read aloud slashes/strokes? What about the phrase "in inverted commas"?
"Over" is, in any case, widely used and understood. I would definitely go with this in the general case.
Because of this I like to say:
- "Three-hundred thirty-four by eleven" for 334/11
When I first read this, my brain went 'no, don't do that, "by" means "times."' And it certainly can mean "times." Although its most common usage is in dimensions. If you said to me "334 by 11" out of context, I'd assume you were talking about something rectangular.
However, after pausing for thought, I realised that "by" does get used for fractions. It's quite common when using radians - if you know what they are? So sin(π/4) would be read "sine pi by four."
Additionally, the notation for the derivative dy/dx is usually read by us Brits as "dy by dx". This is not a fraction, and the people over at math.SE would lynch me if I didn't stress that, but I think it's worth mentioning.
I would say "by" is far too ambiguous for general, out of context usage, especially with plain fractions. As your question seems to imply, you know people use "over" and you are inclined to use it too. So use it. Don't overthink it. The key to successful communication is to use the words that people in your speech community will understand and expect to hear - not to use the words you've decided you think they should use.
Sometimes I use the inflection "-ths" after any number, but I worry this sounds unusual. For example:
- "Three-hundred thirty-four elevenths" for 334/11
But I worry this might be incorrect.
Strictly speaking, of course, this is fine, although have fun with 334/21 and 334/22, for example, but it's pretty clunky as, clearly, you realise. The bigger the denominator, the sillier it gets.
Is there an accepted standard way
Yes. "Over." Well, of course, I should stress that's based on my experience of a good few years in maths classrooms in London, England. Other people may do things differently, but the wording of your question really makes it sound like people in your part of the world also use "over." This is also very much "the standard way", you will get "by" used with some fractions, e.g. the angle π/4 radians (see above). There may even be a rule I'm just not yet familiar with. But if you're looking for a common-or-garden reading that's unambiguous and always works: just use "over"
Best Answer
After a long debate, it's clear that almost everyone normally writes in words
A = -log(X)
as either of:There is also evidence that some people use one exclusively over the other. It looks like British English favors the former (minus), while American English favors the latter (negative).
The following are also used, albeit not formally accurate:
The reason for the inaccuracy is that there is only one logarithm, not one positive and one negative from which you could choose. However, this usage seems okay in some contexts, especially those in which logarithms are multiplied by -1 all the time (Chemistry's pH, for instance).
In spoken language, the same is true, often shortening the logarithm of to simply log and the like.
In order to avoid giving the impression that the final result of
-log(X)
is negative, however, some (not many) authors will use:This is much less popular than the other choices, and some people may mistake its meaning for
exp(X)
rather than-log(X)
.Conclusion
Do use minus/negative the logarithm in general writing and speaking as it is much more current and understood by almost everyone, while also being formally accurate. In special contexts where the resulting sign issue might be a concern (perhaps elementary algebra), it may be more effective to address the possible misconception in an additional note than to resort to the opposite of form.
References for the unpopular opposite of variation:
http://en.wikipedia.org/wiki/Plus_and_minus_signs#Minus_sign
http://www.google.com/search?q="opposite of the logarithm"