No, it is not.
Since that's a fairly small set, you should be able to check all combinations (for 2 numbers, there are only 4 possible multiplications), and see whether the result is in the set.
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
division
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
square
No.
aye
In mathematics, an interval is a set of numbers that contains all numbers between any two numbers in that set. Intervals can be classified as open (excluding the endpoints), closed (including the endpoints), or half-open (including one endpoint but not the other). For example, the interval [a, b] is closed and includes the endpoints a and b, while (a, b) is open and does not include them. Intervals are commonly used to represent ranges of values on the number line.
This is called an interval. An interval includes all real numbers between a specified starting value and ending value, which can be expressed in various forms such as closed intervals (including the endpoints), open intervals (excluding the endpoints), or half-open intervals. Intervals can be finite or infinite, depending on the values specified.
Assuming its endpoints are not equal, a closed interval of the real number line a has an infinite number of real numbers in it. Closed intervals of other ordered sets can have either a finite or an infinite number of elements. I am not sure I answered your question because I am not exactly sure what you are asking. Could you be more specific? Are you talking about a closed interval of the real number line or closed interval of some other ordered set? By finite do you mean 'containing a finite number of elements' or do you mean 'bounded by a finite number'.
Open interval does not include its end points while closed interval includes
There is more than one notation, but the open interval between a and b is often written (a,b) and the closed interval is written [a,b] where a and b are real numbers. Intervals may be half open or half closed as well such as [a,b) or (a,b]. For all real numbers, it is (-infinity,+infinity), bit use the infinity symbol instead (an 8 on its side).
An interval on the number scale is a set of numbers between two end-point. Thus the closed interval [a, b] comprises all number between a and b as well as the two end points. An interval is open if neither end point is included, and semi-open (or semi-closed) if one end in included and the other is not.
Yes, if it is the closed interval. No, if it is the open interval.
A function that is continuous over a finite closed interval must have both a maximum and a minimum value on that interval, according to the Extreme Value Theorem. This theorem states that if a function is continuous on a closed interval ([a, b]), then it attains its maximum and minimum values at least once within that interval. Therefore, it is impossible for a continuous function on a finite closed interval to not have a maximum or minimum value.
An interval in mathematics is a set of numbers that contains all numbers between any two numbers in the set. It can be represented on a number line as a continuous section between two points, often denoted in notation such as [a, b] for a closed interval (including endpoints a and b) or (a, b) for an open interval (excluding endpoints). Intervals can also be infinite, like (-∞, b) or (a, ∞). Visually, an interval appears as a line segment or ray depending on its type.
Probability of an even must lie in the closed interval [0, 1].Probability of an even must lie in the closed interval [0, 1].Probability of an even must lie in the closed interval [0, 1].Probability of an even must lie in the closed interval [0, 1].