Pure math symbols defined

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  • Thread starter houlahound
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  • #1
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Main Question or Discussion Point

looking at notes on functional analysis for self study. the authors I have stumbled across so far launch straight into the formal theory. I can't find any middle ground of intuitive motivations for the theory as yet. I am assuming the following is part of set theory? I can't follow the arguments because I don't know the terminology. are there lists defined for example the symbols in the following. I do not want these particular ones defined I want to know how to do it myself.

what branch of math do I need to read to get a foundation in this language.

any recommended readings.

thanks any leads.



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Answers and Replies

  • #2
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The \ symbol is "set difference" so A \ B = A ∩ BC (the elements of A intersected with the complement of B)

α Fα means ##F_{\alpha_1} \cap F_{\alpha_2} \cap \dots F_{\alpha_n} \cap \dots##, where the ##\alpha_i##s are some indexing set.
α Fα is similar, but is the union over some indexing set.

Books on analysis usually define these symbols in an appendix.
 
  • #3
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α Fα means ##F_{\alpha_1} \cap F_{\alpha_2} \cap \dots F_{\alpha_n} \cap \dots##, where the ##\alpha_i##s are some indexing set.
Correct, but this gives the impression that the number of ##F_\alpha## is countable, while it can be much more general. In any case, it seems the OP will need to look at some basic set theory before he can handle analysis.
 
  • #4
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Correct, but this gives the impression that the number of ##F_\alpha## is countable, while it can be much more general.
Yes, I realize that the ##\alpha##'s are some indexing set, not necessarily a countable set. My intent was to expand the notation somewhat.
 
  • #5
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Does analysis solve problems or just prove theorems and provide tools for solving problems?

ETA, I am going to do classical analysis on real numbers first re calculus. Seems like the logical thing and apparently I am already familiar with many of the content eg limits, series, real numbers etc.

Then set theory/logic then analysis.

Sound sound?
 

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