The linear discrete time interval is used in the interpretation of continuous time and discrete valued: Quantized signal.
A variable defined on a continuous interval as opposed to one that can take only discrete values.
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.
No. If the variable is continuous, for example, height or mass of something, or time interval, then the set of possible outcomes is infinite.
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.
Yes.
A variable defined on a continuous interval as opposed to one that can take only discrete values.
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.
continuous reinforcement - giving a reward every time a desired action is presented
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)
No. If the variable is continuous, for example, height or mass of something, or time interval, then the set of possible outcomes is infinite.
Yes, it is a Continuous variable measured along an equidistant scale.
An interval is the spacing of time. For example: I ran for an interval of 10 minutes then walked for an interval of 30 minutes. Or each car has an interval of 0.5 seconds.
Interval .
Time interval is the period of time between the start and end of an activity.
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.