How do I google this? (f: A -> B)

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Discussion Overview

The discussion revolves around how to effectively search for information related to the notation f: A → B, particularly in the context of mathematics. Participants explore the potential meanings and contexts of this notation, including its relation to functions and category theory.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks guidance on how to search for information about f: A → B, expressing uncertainty about its relation to sets.
  • Another participant suggests using specific search phrases like "a function f from A to B" or "a function f:A->B" to yield more relevant results, noting the generality of the term.
  • A third participant emphasizes that the notation does not necessarily pertain to sets and could represent a morphism in category theory, indicating that the meaning of f: A → B is context-dependent.
  • Participants discuss the importance of defining properties when searching for specific functions, suggesting that adding context can refine search results.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of f: A → B, with some focusing on its function-related aspects while others highlight its potential categorical implications. The discussion remains unresolved regarding the specific context and meaning of the notation.

Contextual Notes

Limitations include the ambiguity of the notation without context, as well as the broad applicability of the term across different areas of mathematics.

Pithikos
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I want to find information regarding what f: A [tex]\rightarrow[/tex]B is. What shall I google? I am not even sure this has anything to do with sets :S
 
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Pithikos said:
I want to find information regarding what f: A [tex]\rightarrow[/tex]B is. What shall I google? I am not even sure this has anything to do with sets :S

You could put "a function f from A to B" of "a function f:A->B" into Google, however this is a very general statement. I would imagine you'll get a whole slew of search results, because that expression is used nearly everywhere in mathematics.

Is it a specific function that you're interested? If so you need to consider its defining properties. If you put a "f:A->B such that ..." (where ... represents the defining property of such a function) into Google, you'll likely narrow the search. The Wiki article that micromass posted is very comprehensive and easy to understand -- I've used it many times.
 
It does not necessarily have to do with sets. It could represent an arrow (also called morphism) between objects in a category. A priori "f:A->B" has no meaning. The context should make clear what the author is talking about.
 

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