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batballbat
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why arent non continuous functions in an interval a linear space?
batballbat said:why does f+g have to be continuous?
A non-continuous function is a mathematical function that has at least one point where it is not defined or is discontinuous, meaning there is a break or jump in the graph of the function.
A function is considered non-continuous if it has any of the following characteristics:
- It has a point of discontinuity, where the function is not defined.
- It has a jump discontinuity, where the function has a sudden change in value.
- It has a removable discontinuity, where the function has a hole or gap in the graph.
- It has an infinite discontinuity, where the function approaches positive or negative infinity at a certain point.
Exploring non-continuous functions in an interval helps us understand the behavior of a function and how it changes within a specific range of values. It also allows us to identify and analyze any discontinuities in the function, which can provide insight into its properties and applications.
Non-continuous functions differ from continuous functions in that they have points where they are not defined or have a break/jump in their graph. Continuous functions, on the other hand, are defined for all values within a given interval and have a smooth, unbroken graph.
To graph non-continuous functions, we first identify the points of discontinuity and mark them on the graph. Then, we graph the function as normal, making sure to leave a gap or break at the points of discontinuity. Additionally, we can use different graphing techniques, such as piecewise functions, to accurately represent the function's behavior and discontinuities.