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seeker101
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I can intuitively see why the sum of two http://en.wikipedia.org/wiki/Simple_function#Definition" is also simple. But can someone point me to a formal proof?
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seeker101 said:I can intuitively see why the sum of two http://en.wikipedia.org/wiki/Simple_function#Definition" is also simple. But can someone point me to a formal proof?
seeker101 said:Sorry. I left something out.
Suppose now the definition of a http://en.wikipedia.org/wiki/Simple_function#Definition" also requires the events [tex]A_k[/tex] to be mutually exclusive.
How can we now show that the sum of two simple functions will also be simple?
The sum of two simple functions can produce another simple function because simple functions are defined as having a finite number of operations and constants. When two simple functions are added together, the resulting function will also have a finite number of operations and constants, therefore it is also a simple function.
No, the sum of two simple functions can never result in a complex function. As mentioned before, simple functions are defined as having a finite number of operations and constants. Complex functions, on the other hand, have an infinite number of operations or constants, which is not possible to obtain from the sum of two simple functions.
Yes, there is a limit to the number of simple functions that can be added together. This limit is determined by the maximum number of operations and constants that can be included in a simple function. Once this limit is reached, the resulting function will no longer be considered a simple function.
No, the sum of two simple functions will always produce a function that is continuous. This is because simple functions are defined as having a finite number of operations and constants, which means there are no breaks or jumps in the function. Therefore, adding two simple functions together will not introduce any discontinuities.
Yes, there are some exceptions to this rule. If one or both of the simple functions being added together are not well-defined or have infinite values, the resulting function may not be considered a simple function. Additionally, if the two simple functions have different domains, the resulting function may not be considered a simple function. In these cases, the sum of two simple functions would not result in a simple function.