Math review = =

Source: Internet
Author: User

This year is not a good year to grow. Just a few basic ways to learn.

 This article marks0] x:p x type is P1] F (x) denotes a function2] (n_1,n_2,...) Represents a multivariate group, in particular, (n) represents a unary group3] x denotes an algebraic symbol/unknown number/variable, i.e. X:UNM4] {...} Represents a collection (usually unordered)-{expr|x in Set} represents a collection of expr executed on each element of the set, i.e.set2<-{expr|x in Set} at this time, expr is one of the set's mappings of elements x to Set2 in set, recorded asExpr:mapper ((Set,x,set2))-Specifically, the set of symbols is recorded as UNM (Universal names), and the collection of all collections is credited as ALS (all sets)1[e] The type of function:-F (x: (set:als)):(set2:als) (for f:fun< (x: (set:als)):(set2:als) > abbreviated)abbr. f (x): Set->set2-a type of function constituent set {(F:UNM):(set:als) (set2:als)}-Example: Mapper ({(SET:ALS,SY:UNM,SET2:UNM)}): {(F:UNM):(Sy:set) (Py:set2)}5] [...] Represents a vector/matrix (depending on context)6] Representation of certain sets- R/rr real number set- Q/qq Rational Number set- Z/zz Integer Collection- C/cc Complex set-Generalized, multivariate set of numbers will be credited as <bS_1,bS_2...>i.e. C=<R,r>A two-dollar integer will be credited as Cc^z=<zz,zz>-n-th polynomial set is credited as Poly<n:zz>-The polynomial is denoted by a symbol of a function set (X:UNM) (poly<n:zz>)7] The expression of the limit-lim{x->n} (expr)as-LIM{X:UNM->N:RR} (p:poly<d:zz>) =p (x)8] = and <- and  - = denotes meaning equal or strictly equal- <- expression Assignment-  --is a token of the function return value* denoted as meaning equals9] Operator-+-*/^ and other common10] Abuse of parenthesesNo offense .
1. Extreme Thinking

We have a function f (x): Rr->rr.

function, people who have probably learned to program are recognized. But the computer's function and the mathematics ratio, has the extension aspect, also has the inferior aspect.

A single-variable function can be seen as a mapping of a collection to another collection. Similarly, there is no difference in multivariable functions because we can classify it as a multivariate group.

In most cases, the value off (x) is computable. Indeed, when F (X:RR): X (poly<n:zz>) , it is computable. But back to this equation, the typical "error" Equation:

1/0

Its value cannot be calculated. We simply refer to this value as NaN or ccinf. or throw an error directly.

NaN is a very special value. Nan{operator} (p:als) =nan. You might say this is infinite oo. Actually, it's not. Oo is a number-shaped notation of a process. oo does not equal any number.

So let's look at these two functions f (x) =e^x and g (x) =sin (x) x/X.

f (x) =e^x ($f (x) =e^x$) is a common example that can be evaluated at any point in the scope of a function. g (x) =sin (x)/ X ($g (x) =\frac{\sin{x}}{x}$) seems to be everywhere, but meaningless in x=0 .

Math review = =

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