If expr1 does not exist, or is null, the value of $x is expr2. The value of $x is expr1 if expr1 exists, and is not null. The value of $x is expr3 if expr1 = false The value of $x is expr2 if expr1 = true. Var_dump($x $y) // Outputs: boolean trueĬonditional assignment operators are used to set a value depending on conditions. Var_dump($x != $y) // Outputs: boolean true Var_dump($x = $y) // Outputs: boolean false True if $x is greater than or equal to $y True if $x is not equal to $y, or they are not of the same type True if $x is equal to $y, and they are of the same type Whenever we want to compare the data types of the two given values regardless of whether the two values are equal or not, we make use of not equal operator in PHP. OperatorĬomparison operators are used to compare two values in a Boolean fashion. One of the comparison operators in PHP is not equal, which is represented by the symbol or <>.The PHP arithmetic operators are used in conjunction with numeric values to perform common arithmetic operations such as addition, subtraction, multiplication, and so on. For example, the addition ( +) symbol instructs PHP to add two variables or values, whereas the greater-than ( >) symbol instructs PHP to compare two values. 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.Operators are symbols that instruct the PHP processor to carry out specific actions. 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. Its mandatory in mainstream languages, however it. 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. is used in comparisons when you have to check if two values are equal. 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. 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. 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. It is important not to confuse it with the (single. ![]() The approximation sign "≈" I use for decimal approximations with tilde "~" being a rougher approximation. As already encountered a few times in this chapter, the equality operator is (two equals signs). 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. But I realized that if (foo bar) is correct too. 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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