A 1-dimensional interval (a, b) is continuous if for any k in (0, 1) the point a + k*(b-a) = a*(1-k) + k*b is also in the interval.
This is equivalent to the statement that every point on the line joining a and b is in the interval.
The above can be extended to more dimensions analogously.
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.
A variable defined on a continuous interval as opposed to one that can take only discrete values.
Yes, it is a Continuous variable measured along an equidistant scale.
The linear discrete time interval is used in the interpretation of continuous time and discrete valued: Quantized signal.
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.
Yes.
A variable defined on a continuous interval as opposed to one that can take only discrete values.
If the function is continuous in the interval [a,b] where f(a)*f(b) < 0 (f(x) changes sign ) , then there must be a point c in the interval a<c<b such that f(c) = 0 . In other words , continuous function f in the interval [a,b] receives all all values between f(a) and f(b)
Yes, it is a Continuous variable measured along an equidistant scale.
Yes, land area is considered an interval variable because it can be measured on a continuous scale with equal units between values.
why doesn't wiki allow punctuation??? Now prove that if the definite integral of f(x) dx is continuous on the interval [a,b] then it is integrable over [a,b]. Another answer: I suspect that the question should be: Prove that if f(x) is continuous on the interval [a,b] then the definite integral of f(x) dx over the interval [a,b] exists. The proof can be found in reasonable calculus texts. On the way you need to know that a function f(x) that is continuous on a closed interval [a,b] is uniformlycontinuous on that interval. Then you take partitions P of the interval [a,b] and look at the upper sum U[P] and lower sum L[P] of f with respect to the partition. Because the function is uniformly continuous on [a,b], you can find partitions P such that U[P] and L[P] are arbitrarily close together, and that in turn tells you that the (Riemann) integral of f over [a,b] exists. This is a somewhat advanced topic.
Yes, skin temperature in degrees centigrade is considered interval data. Interval data is continuous data that has a meaningful zero point, but ratios between values are not meaningful. Skin temperature can be measured on a continuous scale with a specific unit of measurement (degrees centigrade) where a value of zero does not indicate absence of skin temperature.
The contour interval
You can determine whether an interval is major or minor by counting the number of half steps between the two notes. If the interval has a distance of 2, 3, 6, or 7 half steps, it is major. If it has a distance of 1, 4, 5, or 8 half steps, it is minor.
sorry but are gone mad
Interval training is periods of work followed by periods of rest. This is known as work:rest ratio. This is commonly used to train the anaerobic energy system. Continuous training, of which there are many forms does not involve rest periods, although it could involve periods of different intensities (such as Fartlek training).
well there is weight training, fartlek,continuous, interval , circuit, flexibility and weight