What Distinguishes Distributions from Functions?

AI Thread Summary
A distribution is defined as a functional, which means it maps a set of functions to a field of numbers. This distinguishes it from a traditional function, which directly relates inputs to outputs. Distributions can handle more generalized cases, such as those involving singularities or discontinuities, where standard functions may not apply. The discussion seeks more intuitive explanations to clarify this concept further. Understanding the distinction is crucial in fields like mathematics and physics, where distributions play a significant role.
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What is the difference between a distribution and a function?
 
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A distribution is a functional, i.e. a mapping from a set of functions to a field of numbers.

Daniel.
 
dextercioby said:
A distribution is a functional, i.e. a mapping from a set of functions to a field of numbers.
I see. Any alternative explanations? More intuitive ones perhaps?
 

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