1,314 reputation
416
bio website mathematics21.org
location
age
visits member for 3 years, 7 months
seen Jul 20 at 23:54

An amateur general topology researcher.


Jun
22
accepted A property of co-brouwerian lattices
Jun
22
asked Help to conceive a name
Jun
21
revised Defining principal elements of every poset. Is this a new idea?
added 5 characters in body
Jun
21
revised Defining principal elements of every poset. Is this a new idea?
added 116 characters in body
Jun
21
comment Defining principal elements of every poset. Is this a new idea?
@OlivierBégassat: See "Moreover, my idea can be generalized from complete lattices to arbitrary posets..." near the bottom of my question
Jun
21
comment Defining principal elements of every poset. Is this a new idea?
@OlivierBégassat: Yes, but only for lattices with a bottom element, not for arbitrary posets. My definition is valid for any posets
Jun
21
comment Defining principal elements of every poset. Is this a new idea?
@OlivierBégassat: Thanks, corrected
Jun
21
revised Defining principal elements of every poset. Is this a new idea?
a formula corrected
Jun
21
revised Defining principal elements of every poset. Is this a new idea?
added 60 characters in body
Jun
21
asked Defining principal elements of every poset. Is this a new idea?
Jun
20
comment Writing a chain of implications in English
@DanPiponi: A reader may be misguided (especially when we say "four assertions") by the fact that the last (fourth) "assertion" is supposed to imply an empty set of "following ones"
Jun
20
comment Writing a chain of implications in English
@DanPiponi: Will "Each of these assertions implies the following ones:" before a numbered list clear by itself (even for beginning students)? Or does this need further clarification?
Jun
20
comment Writing a chain of implications in English
Hm, I may write "The following is a tuple of implications: (1) ... (2) ... (3) ... (4) ..." and define "tuple of implications" near the beginning if my book (as a tuple of logical formulas, every of which (except of the last) implies the next)
Jun
20
comment Writing a chain of implications in English
Saying it one time wouldn't insult. But I want to repeat it in many (maybe around 50, I haven't calculated) theorems in the book I write. Repeating this phrase every time would be not good
Jun
20
comment Writing a chain of implications in English
@SantiagoCanez: If I break my theorem into multiple ones, the reader would need to check that the result $B$ in the first theorem is the same as condition $B$ in the second theorem. $B$ may be a complex expression and I do not want to force the reader to compare two instances of $B$ to be sure they are the same
Jun
20
comment Writing a chain of implications in English
@SantiagoCanez: I mean $(A \Rightarrow B) \wedge (B \Rightarrow C) \wedge (C \Rightarrow D)$. I don't want to break the theorem into pieces, it is the reason why I ask about this
Jun
20
comment Writing a chain of implications in English
I was suggested "Consider the following assertions. (Statements of (a)...(d)) Then the implications (a) => (b) => (c) => (d) hold."
Jun
20
asked Writing a chain of implications in English
Jun
10
asked Quantifiers bind tightly?
May
27
comment Choosing from two index families of sets
I've solved it positively. My proof uses somehow advanced operations on filters. The proof is in mathematics21.org/binaries/staroids2.pdf