true
Yes. A function is a rule to assign a value based on some other value; you can make the function equal to a constant for all values of a variable "x", or you can make it equal to a few values. Commonly used functions of this type include the integer function (take the integer part of a number), which, if you consider a finite domain (for example, all numbers from 0 to 10), has an infinite number of values in the domain, but only a few specific values in its range; and the sign function.
The number of elements of a pid may be finite or countably infinite...or infinite also....but a finite field is always a pid
A number does not have a range and domain, a function does.
Not necessarily. There are series over all kinds of subsets and supersets of the set of real numbers.
No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
The domain is the possible values that can be input into the function and produce a real number output.
f(x)=5x Domain is any number for x that will provide a real number for f(x). In this function, x can be any real number, and f(x) will be a real number. Thus domain is all real numbers.
Yes. The domain and range can include irrational numbers.
It is a finite number.It is a finite number.It is a finite number.It is a finite number.
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Sure. Remember that a function is ANY rule defined to calculate one number based on another number. You can define such a rule any way you want. For example, you can have a function which for ANY value in its domain, the result will always be 1 (or any other number you choose). Such a function (the constant function) will fulfill the requirements of the question. A more interesting (and more useful) example is the "sign" ("signum") function, defined with the following rule: * For x < 0, f(x) = -1 * For x > 1, f(x) = 1 * For x = 0, f(x) = 0 This function has only three values in its range.
yes it is a function because sequence defined as "a function whose domain is set of natural number"