![]() This mostly makes the code easier to read and maintain. It is also presumably a good candidate for a function. Not a have to but a would strongly consider. It will also make it easier to spot which is what. Though that one is safe, if you have as habit using all upper case, one day you might say IFS="boo" and you're in a world of hurt. This is to prevent collision between variables introduced by the system, which almost always is all upper case. Whereas you tried to do: not (A B C) > not (A) not (B) not (C) Which obviously doesn't work. What type of test one choose to use is highly dependent on code, structure, surroundings etc.Īn alternative could be to use a switch or case statement as in: case "$PHONE_TYPE" inĮcho "Phone type must be nortel,cisco or nec"Īs a second note you should be careful by using upper-case variable names. The rules for these equivalents are called De Morgan's laws and in your case meant: not (A B C) > not (A) & not (B) & not (C) Note the change in the boolean operator or and and. Setting f(x) to zero creates the equivalency f(x) = 0 for the coordinate you are trying to solve but is not true for all coordinates that are solvable.Good answers, and an invaluable lesson ) Only want to supplement with a note. I use ≡ for all cases, not only immediate ones. For a quadratic I would set f(x) to zero but would not define f(x) as zero. I am using it to state a relationship to find sums instead of stating it as the sum that we are deriving however it can be used to state equivalence. Triangle 3/4/5 is ≅ to triangle 4/5/3 the difference being a rotation changing the coordinates of the angles but preserving angle and side length.Īlso I use the definition symbol "≡" to define functions. That is why laymen or service professionals are free to explore it and academics prefer something more clearly defined unless deformations are allowed as in my case. Here’s some examples of how Not Equal looks in common Office fonts. The official Unicode name is ‘ Not Equal To ’. As such this is not a popular use and purists and rigorous math profs disdain it because they do not have a way of using it or defining it soundly. Not Equal symbol is used in equations, obviously but it’s also handy shorthand in a heading or slide. 3/4 does not equal 3.1/4.1 but could be rough approximations for something already constructed. Real life triangles use approximations and have rounding errors. I write ▲ABC ~ ▲A'B'C' where ▲A'B'C' is a dilated version of the pre-image.įor a closer similarity "≃" might mean a triangle almost congruent but only ROUGHLY similar, such as two triangles 3/4/5 and 3.1/4.1/5.1 while "≅" means congruent. Tilde "~" I use to state a geometric shape is similar to another one ie a triangle of sides 3/4/5 is similar to a triangle with sides 30/40/50. The approximation sign "≈" I use for decimal approximations with tilde "~" being a rougher approximation. In my work "=" is the identity of a number so it states an equivalence. The main take-away from this answer: notation is not always standardized, and it's important to make sure you understand in whatever context you're working. The $\approx$ is used mostly in terms of numerical approximations, meaning that the values in questions are "close" to each other in whatever context one is working, and often it is less precise exactly how "close." Topologists also have a tendency to use $\approx$ for homeomorphic. I've seen colleagues use both for isomorphic, and some (mostly the stable homotopy theorists I hang out with) will use $\cong$ for "homeomorphic" and $\simeq$ for "up to homotopy equivalence," but then others will use the same two symbols, for the same purposes, but reversing which gets which symbol. Both are usually used for "isomorphic" which means "the same in whatever context we are." For example "geometrically isomorphic" usually means "congruent," "topologically isomorphic" means "homeomorphic," et cetera: it means they're somehow the "same" for the structure you're considering, in some senses they are "equivalent," though not always "equal:" you could have two congruent triangles at different places in a plane, so they wouldn't literally be "the same" but their intrinsic properties are the same. The notations $\cong$ and $\simeq$ are not totally standardized.
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