The single tick following a variable is often (but not always) used to represent a derivative and (in the United States) is always pronounced "prime." In your example, "Ex prime = ex plus tee."
f(x) = x² <--- "Eff of ex equals ex squared."
f′(x) = 2 x <---- "Eff prime of ex equals two ex."
f′′(x) = 2 <---- "Eff ...
It would normally be read aloud as:
f of x equals x squared
There are some variations you might hear. For example, sometimes is is used in place of equals.
If the exponent was 3, you would say cubed. Anything higher than three (say, for example, 5) would generally be read aloud as:
f of x is x to the fifth (power)
f of x is x to the ...
In this context, "cherry-picking" is a very negative term. This meaning comes from statistical analysis. The term is idiomatic and informal. It is not as negative as accusing someone of lying, but it strongly implies that they do not care whether they mislead.
Suppose you are writing an article about a sports team. The team won its first game, lost its ...
Here's how I'd say the first one:
The absolute value of S minus the sum from 1 to n of f of t sub i times delta sub i is less than epsilon.
(1) The absolute value of
(2) S minus
(3) the sum from 1 to n of
(4) f of t sub i
(5) times delta sub i
(6) is less than epsilon
Note: Some mathematical expressions can be read aloud in ...
The fractional part of a number is known as the Mantissa.
The mantissa is defined as the positive fractional part of a real number.
Your suggestion of decimal places is usually used to specify a number of digits that must follow the decimal point. The term mantissa makes no such restriction. It defines all the digits after the decimal point.
We use the expression "anecdotal evidence". This doesn't have to mean a sample size of one (but it could) it does mean that the sampling was informal, and the data was based on personal testimony.
Mary said that using baking soda had cleared up her acne, but that's just anecdotal evidence. We organised a clinical trial to test the effectiveness.
You have several options:
one point five
one and a half
one and one-half - can seem wordy.
one and five-tenths - mathematically correct term, not used regularly.
These are all correct.
The hyphens in the last two are optional to some degree depending on the source. Including it is arguably more correct.
one and half is not correct... usually. Based on ...
A composite number is a positive integer that can be formed by multiplying together two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers ...
There's no word that I'm aware of that means a third of a circle. We have quadrant (1/4), sextant (1/6) and octant (1/8) but nothing for a third beyond the generic term: a sector.
You could call it a one-third sector or a 120 degree sector.
Based on numerical prefixes, if there was such a word it would be 'tridant' but this isn't a word you'll find in any ...
How you explain this really depends on how much you want to convey, and how much you think will be assumed. For instance, the most specific wording of the first example would go something like this:
One plus open parenthesis negative two close parenthesis equals negative one.
The second example would be as follows:
One minus two equals negative one.
The absolute value of the difference between S and
the sum from i equals one through i equals n of
the function f evaluated at t sub i times the width of each i
is less than epsilon.
If it is clear that i and n are one-indexed, then "the sum from i equals one through i equals n" can be replaced by "the sum of the first n terms". "The width of each ...
While one meaning of "may" is "be in some degree likely to", in this case the meaning is probably "have permission to". Assuming the latter definition, the statement means that students are not allowed to borrow more than three books in one month.
Let us assume x is real
This sounds about right.
Let us assume x be real
This is grammatically incorrect.
Let us assume x to be real
This is grammatically correct, but sounds awkward, though with more context, it could be more correct than is.
The precise name of a symbol in mathematics sometimes depends on what you're using it for. For example, × is often referred to simply as the multiplication sign, but if you need to distinguish scalar from vector multiplication, you might refer to it more specifically as the cross multiplication sign, vector multiplication sign, or something similar.
There is a shade of meaning.
Minkowski space is a mathematical entity that can be studied and applied to several different cases, but there is one specific case which stands out, as this entity describes the space-time in which "the laws of nature" are elegantly described (as part of Einstein's special relatively theory).
So when you talk about "the ...
Exists and exist follow the ordinary convention for verbs: one is singular and the other is plural. Where mathematical usage differs from ordinary usage is in the way singular and plural are indicated in the subject that follows, and an implied “for all” later if the subject is plural.
Exists is singular:
There exists s'' in S such that s''(s'm – sm') = ...
Formally, The derivative of...
Y equals the sine of f-of-x, implies that the derivative of y equals cos f-of-x times the derivative of f of x.
Informally, and depending on dialect, you can say either 'prime' (as per Humbulani's answer) or 'dash' - f prime of x, y-dash etc. The former is predominant in (but is not restricted to) the US, while the ...
f prime of x, or
the derivative of f of x, or
the derivative of f with respect to x.
f double prime of x, or
the second derivative of f of x, or
the second derivative of f with respect to x.
x dot, or
the derivative of x with respect to time, or
the time derivative of x.
If x is a distance, ẋ can ...
In a formal mathematics setting, you would say you want the number with the smallest magnitude. For real numbers, magnitude is the number's distance from zero on the number line. You could also say you want the number with the smallest absolute value, but that's slightly longer to say.
Using "minimum" is incorrect, since for real numbers, "...
It depends on your audience.
With any mathematical audience, you can write:
A is the negative of the logarithm of X.
In speech, you can also say:
A is minus the logarithm of X.
A is the negative of log X.
A is minus log X.
People who work with very small numbers
Some mathematically knowledgeable audiences work a lot with ...
The first version is ambiguous. In a mathematics course, it would be considered incorrect for this reason.
As you state in your question, the phrase times faster than could be taken to mean a multiplicative increase (A = 1.75B) or an additive increase (A = 1.75B + B).
By using the phrase times as fast as you are eliminating the possibility of the increase ...
an aspect of 120° (one third of a circle).
However this is a fairly obscure word, I think.
Edit: upon further inspection it appears this word refers to a group of three, not a single third.
trine (trīn) n.
A group of three.
In astrology, the aspect of two planets when 120° apart.
It depends on context.
For scalar values (all "normal" numbers that we know and love are scalar), all of those operators are the same, and are called multiplication, and the operator is called the multiplication operator, or much less frequently as the times operator.
When reading the equation "3 x 2" out loud, natives would typically use the following ...
Absolute value of s minus sum i equals one to n, of f of t i times delta i, is less than epsilon.
Integral from zero to infinity of dx by x plus one times square root of x is equal to the limit of integral from s to one of dx by x plus one times square root of x as s tends to zero plus the limit of integral from one to t of dx by x plus one times square ...
Although not a direct answer to your question, here are a few references on how to read mathematical symbols and expressions. As a non-native English speaker who has to read mathematical formulae, I've found them pretty useful.
Handbook for Spoken Mathematics, Research and Development Institute, Inc: This is probably the most complete reference. Not of easy ...