What is the meaning of g: [a, b] → R in set notation?

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The notation g: [a, b] → R indicates that the function g is defined on the interval [a, b] and maps to the real numbers R. There is some discussion about the interpretation of the arrow (→), which may signify "into" rather than "onto." Users express difficulty in finding updated resources on this notation. One participant found useful information in an introductory real analysis textbook. Understanding this notation is essential for grasping function definitions in mathematics.
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I've been looking around a few places to try to understand some notation. I'm not sure exactly what to call it(set notation?) but basically things like g: [a, b] → R and stuff like that. I think it means something like g is defined on [a,b] in the real numbers, but is there a resource I can use to learn this type of notation?
 
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Hi RM:

I think your interpretation of the example is correct. However, the → might mean into rather than onto.

Unfortunately, notations have changed since I learned them, and I can't suggest any references.

Good luck.

Regards,
Buzz
 
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Thanks. I ended up finding the information in an intro to real analysis, which looks like it has everything I need.
 
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