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Here are some other definitions for term. Textbook Elementary Algebra, "A term is either a single number (called a constant term) or the product of a number and one or more variables." Thus $2(x-y)$ is not a term. Most textbooks give statements like "To subtract a sum of terms, change the sign of each term and add the results."
2. In "Introduction to functional differential equations" by Hale and Lunel (1993), I found the following definition of principal term. Let P(z, w) P (z, w) be a polynomial of the form. P(z, w) =∑m=0r ∑n=0s amnzmwn. P (z, w) = ∑ m = 0 r ∑ n = 0 s a m n z m w n. We call arszrws a r s z r w s the principal term of the polynomial if ars ...
y:= 7x + 2 y:= 7 x + 2. means that y y is defined to be 7x + 2 7 x + 2. This is different from, say, writing. 1 =sin2(θ) +cos2(θ) 1 = sin 2 (θ) + cos 2 (θ) where we are saying that the two sides are equal, but we are not defining "1" to be the expression " sin2(θ) +cos2(θ) sin 2 (θ) + cos 2 (θ) ". Basically, some people think that there ...
An interval is a subset of a set of numbers S that has an ordered pair of endpoints (l, r) where l ≤ r. l is called the left endpoint of the interval, while r is called the right endpoint of the interval. An interval contains no members which are less than its left endpoint, and no members which are greater than its right endpoint.
A Numerical System is the representation of numbers through a sequences of digits and other symbols (minus sign, point) B) Number System is sometimes regarded as synonym for Number Set. For me a Number Set is a set with the Natural Numbers as subset. I think it is more than just a set and I would expect additional required properties.
Other symbols used to denote a definition include $$\stackrel{\triangle}= \quad , \stackrel{\text{def}}= \quad, \stackrel{\cdot}= \quad .$$ Whilst there's no amibguity in the latter three symbols, you try typing \stackrel{\triangle}= every single time you make a definition, as opposed to the much-shorter :=. You'll then see why the latter of ...
This is basically the definition you give, with the addition that the term that changes sign has to be an irrational square root of a rational number. However, this is not terribly illuminating about why this is a good definition. The basic idea is the following:
Definition: Theorem, Lemma, Proposition, Corollary, Postulate, Statement, Fact, Observation, Expression, Fact, Property, Conjecture and Principle. Most of the time a mathematical statement is classified with one the words listed above. However, I can't seem to find definitions of them all online, so I will request your aid in describe/define them.
The definition for segments leave out intervals like (1,2) or (1,2]. This is equivalent to saying that an interval is a convex (equivalently, connected) subset of R R which doesn't depend on the behavior at the endpoints. This definition allows you to treat the four different cases more or less the same. – Harry Reed.
In math, for me, there isn't "right" and "wrong" definitions. There's "useful" and "less useful" definitions. "A number divided by zero may be any number" is not a useful definition for me. You can choose to use that definition if you like, but you may find in your career that it is "less useful" than you may have initially thought.