{"id":495,"date":"2015-04-27T18:43:19","date_gmt":"2015-04-27T10:43:19","guid":{"rendered":"http:\/\/xxxsola.org\/?p=495"},"modified":"2015-04-27T21:18:01","modified_gmt":"2015-04-27T13:18:01","slug":"%e6%95%b0%e5%ad%a6%e5%85%ac%e5%bc%8f%e7%9a%84%e8%8b%b1%e8%af%ad%e8%af%bb%e6%b3%95-zt","status":"publish","type":"post","link":"https:\/\/xxxsola.org\/cms\/495.html","title":{"rendered":"[\u8f6c]\u6570\u5b66\u516c\u5f0f\u7684\u82f1\u8bed\u8bfb\u6cd5"},"content":{"rendered":"

1.Logic<\/strong><\/p>\n

\u2203there exist<\/p>\n

\u2200for all\uff08\u770b\u5230\u6709\u4eba\u8bf4\u662ffor any\uff09<\/p>\n

p\u21d2q p implies q \/ if p, then q<\/p>\n

p\u21d4q p if and only if q \/p is equivalent to q \/ p and q are equivalent<\/p>\n

2.Sets<\/strong><\/p>\n

x\u2208A x belongs to A \/ x is an element (or a member) of A<\/p>\n

x\u2209A x does not belong to A \/ x is not an element (or a member) of A<\/p>\n

A\u2282B A is contained in B \/ A is a subset of B<\/p>\n

A\u2283B A contains B \/ B is a subset of A<\/p>\n

A\u2229B A cap B \/ A meet B \/ A intersection B<\/p>\n

A\u222aB A cup B \/ A join B \/ A union B<\/p>\n

A\\B A minus B \/ the diference between A and B<\/p>\n

A\u00d7B A cross B \/ the cartesian product of A and B<\/p>\n

3. Real numbers<\/strong><\/p>\n

x+1 x plus one<\/p>\n

x-1 x minus one<\/p>\n

x\u00b11 x plus or minus one<\/p>\n

xy xy \/ x multiplied by y<\/p>\n

(x-y)(x+y) x minus y, x plus y<\/p>\n

= the equals sign<\/p>\n

x=5 x equals 5 \/ x is equal to 5<\/p>\n

x\u22605 x (is) not equal to 5<\/p>\n

x\u2261y x is equivalent to (or identical with) y<\/p>\n

x>y x is greater than y<\/p>\n

x\u2265y x is greater than or equal to y<\/p>\n

x<y x is less than y<\/p>\n

x\u2264y x is less than or equal to y<\/p>\n

0<x<1 zero is less than x is less than 1<\/p>\n

0\u2264x\u22641 zero is less than or equal to x is less than or equal to 1<\/p>\n

|x| mod x \/ modulus x<\/p>\n

x2 <\/sup>x squared \/ x (raised) to the power 2<\/p>\n

x3 <\/sup>x cubed<\/p>\n

x4<\/sup> x to the fourth \/ x to the power 4<\/p>\n

xn<\/sup> x to the nth \/ x to the power n<\/p>\n

x (\u2212n) <\/sup>x to the (power) minus n<\/p>\n

x\u7684\u5e73\u65b9\u6839(square) root x \/ the square root of x<\/p>\n

x\u7684\u4e09\u6b21\u6839cube root (of) x<\/p>\n

x\u7684\u56db\u6b21\u6839fourth root (of) x<\/p>\n

x\u7684n\u6b21\u6839nth root (of) x<\/p>\n

(x+y)2<\/sup> x plus y all squared<\/p>\n

n! n factorial<\/p>\n

x^x hat<\/p>\n

x\u00af x bar<\/p>\n

x\u02dc x tilde<\/p>\n

xi<\/sub> xi \/ x subscript i \/ x suffix i \/ x sub i<\/p>\n

\u2211(i=1~n) ai<\/sub> the sum from i equals one to n ai<\/sub> \/ the sum as i runs from 1 to n of the ai<\/sub><\/p>\n

4. Linear algebra<\/strong><\/p>\n

\u2016x\u2016the norm (or modulus) of x<\/p>\n

OA\u2192<\/sup>OA \/ vector OA<\/p>\n

OA\u00af OA \/ the length of the segment OA<\/p>\n

AT<\/sup> A transpose \/ the transpose of A<\/p>\n

A\u22121<\/sup> A inverse \/ the inverse of A<\/p>\n

5. Functions<\/strong><\/p>\n

f(x) fx \/ f of x \/ the function f of x<\/p>\n

f:S\u2192T a function f from S to T<\/p>\n

x\u2192y x maps to y \/ x is sent (or mapped) to y<\/p>\n

f\u2019(x) f prime x \/ f dash x \/ the (first) derivative of f with respect to x<\/p>\n

f\u201d(x) f double-prime x \/ f double-dash x \/ the second derivative of f with respect to x<\/p>\n

f\u201d\u2019(x) triple-prime x \/ f triple-dash x \/ the third derivative of f with respect to x<\/p>\n

f (4) (x) f four x \/ the fourth derivative of f with respect to x<\/p>\n

\u2202f\/\u2202x1<\/sub> the partial (derivative) of f with respect to x1<\/p>\n

\u22022<\/sup>f\/\u2202x1<\/sub>2<\/sup> the second partial (derivative) of f with respect to x1<\/p>\n

\u222b0<\/sub>\u221e<\/sup> the integral from zero to infinity<\/p>\n

limx<\/sub>\u2192<\/sub>0<\/sub>the limit as x approaches zero<\/p>\n

limx<\/sub>\u2192<\/sub>0+<\/sub>the limit as x approaches zero from above<\/p>\n

limx<\/sub>\u2192<\/sub>0\u2212<\/sub>the limit as x approaches zero from below<\/p>\n

loge<\/sub>y log y to the base e \/ log to the base e of y \/ natural log (of) y<\/p>\n

lny log y to the base e \/ log to the base e of y \/ natural log (of) y<\/p>\n","protected":false},"excerpt":{"rendered":"

1.Logic \u2203there exist \u2200for all\uff08\u770b\u5230\u6709\u4eba\u8bf4\u662ffor any\uff09 p\u21d2q p impl […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/posts\/495"}],"collection":[{"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/comments?post=495"}],"version-history":[{"count":0,"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/posts\/495\/revisions"}],"wp:attachment":[{"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/media?parent=495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/categories?post=495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xxxsola.org\/cms\/wp-json\/wp\/v2\/tags?post=495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}