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 Jan 19 comment How to write a definition of less than $<$? @TheChaz that can happen in a recursive definition. Jan 12 comment How to solve instant insanity puzzle with graphs. @SteveKass I related your answer to the question "how can I find the path from the graph I attached". Jan 11 comment if the inverse images of all closed balls are closed, is $f$ continuous? +1, I think this work for all f continous in $(0,\infty)$. So you can use a simpler f like f(x)=x or f(x)=1 in your example. Jan 7 comment How to solve instant insanity puzzle with graphs. @SteveKass "Probably not" is probably wrong. Even if it isNP-complete it is possible that it can be solved for input of small size. Jan 7 comment How to solve instant insanity puzzle with graphs. Photos are not useful especially if the numbers cannot be read because they are written to small. Put the data in an appropriate format: 3-column list. The first column is the label of the edge (the cube number) the second is the name of the the vertex of the edge with the smaller number (color) and the third column is the other vertex of the edge. But don't add a photo of the list to the post but add it as code (each line is preceded by four whitespace) so that one can copy and paste the data. Jan 7 comment How to find out the number of ways to solve Instant Insanity In Donald Knuth's paper Estimating the Efficiency of Backtrack Programs you can find an explanation. Jan 5 comment Prove that if Triangles ABC = DEF in a metric geometry, then line AB contains exactly two of the points D, E, and F. "Clearly $\overleftrightarrow{AB}$ cannot intersect any other side at any other point." Any other side of $\bigtriangleup ABC$ or of $\bigtriangleup DEF$ ? Jan 4 comment Prove that if Triangles ABC = DEF in a metric geometry, then line AB contains exactly two of the points D, E, and F. definitions can be found here: math.furman.edu/~dcs/courses/math36/assignments.html Jan 1 comment Shortest distance to a straight line @copper: If it is the same why did you add this "Alternative" paragraph to your post afterwards? Dec 16 comment Go from A to D in three equal steps @Michael: I didn't check this. But the OP shows that there are triples $(a,d,e)$ where at least one solution exists. Dec 16 comment Go from A to D in three equal steps for me it is ok if you edit your question in such a way that it does not invalidate my answer, e.g. you can add, that you prefer a geometric proof. Dec 6 comment What does this ∩ symbol mean in terms of geometry I rolled back the last edit to make the drawing visible again Dec 6 comment What does this ∩ symbol mean in terms of geometry So what means (AB || CD) ∩ CK ? Dec 1 comment How to handle this curve? this is your 7th post. you should start to write you formulas in LaTeX Nov 26 comment Expressing Sets as Regular Expressions @blues5938 I think more important than thinking about "accurracy" is to think how prove that a regular expression exactly represent a given set of strings , e.g. your setof strings defined by 1. or your set of string given by 2. Nov 26 comment Expressing Sets as Regular Expressions I missed your edit. I think wil match all required string, but I will heck this. But the three other patterns are wrong. If the regular expression is correct, it is unclrear what means "more accurate". You must define some measure for accuracy. One possibility is to count the number of characters in a pattern string and say a pattern is more accurate ithan another pattern if it needs less characters. (10∪0)*(λ∪1)00 has length 14, my pattern (10∪0)(10∪0)*0 hs length 14, too so both have the same accuracy if we use this accuracy metric Nov 26 comment Expressing Sets as Regular Expressions I don't know what means 'more' accurate: Either it is accurate or it is not. My regular expressions match exactly that what is required. Your regexp in 1. don't match 100 Nov 26 comment Expressing Sets as Regular Expressions But maybe this is not availible in your syntax. Nov 26 comment Expressing Sets as Regular Expressions Why do you need this? I means 1 can appear at this position. he usual regular epression syntax is 1? for this. Nov 26 comment Expressing Sets as Regular Expressions Can you explain what is λ?