{"id":425,"date":"2021-04-27T04:20:28","date_gmt":"2021-04-27T04:20:28","guid":{"rendered":"https:\/\/enorcerna.com\/wiki\/what-is\/intervals\/"},"modified":"2021-04-27T04:20:28","modified_gmt":"2021-04-27T04:20:28","slug":"intervals","status":"publish","type":"post","link":"https:\/\/enorcerna.com\/wiki\/what-is\/intervals\/","title":{"rendered":"Intervals"},"content":{"rendered":"
\n

What are the intervals?<\/h2>\n

An interval is a set of real numbers that is between two extremes, a and b.<\/strong> It can also be called a subset of the real line.<\/p>\n

For example<\/strong>, the numbers that satisfy a condition 1 \u2264 x \u2264 5<\/strong> or [1;5]<\/strong> they involve a range from 1 to 5, including both.<\/p>\n

If the application of the interval is taken into account to observe the behavior of a variable, a time series is taken and an interval is chosen.<\/p>\n

Classification of intervals<\/h2>\n

There are 4 types of mathematical intervals, these are: open, closed, semi-open and infinite<\/strong>.<\/p>\n

Open interval<\/h3>\n

An open interval is one that does not include<\/strong> the extremes between which it is included, but all the values \u200b\u200blocated between them. It is represented by an expression of the type a or (a; b)<\/strong>.<\/p>\n

For example<\/strong>If we have the open interval (1; 5), we will have the set of numbers greater than 1 and less than 5. Not including 1 and 5.<\/p>\n

\"Representation<\/p>\n

Representation on the real line of the open interval (a; b).<\/p>\n<\/div>\n

Closed interval<\/h3>\n

A closed interval is one that It includes<\/strong> the extremes of the interval and all the values \u200b\u200bbetween them. It is represented by an expression of the type a \u2264 x \u2264 b<\/strong> or [a;b]<\/strong>.<\/p>\n

For example<\/strong>, if we have the closed interval [1;5], we will have the set of numbers greater than or equal to 1 and less than or equal to 5. Including 1 and 5.<\/p>\n

\"Representation<\/p>\n

Representation on the real line of the closed interval [a;b].<\/p>\n<\/div>\n

Semi-open interval<\/h3>\n

A semi-open interval is one that includes only one of the extremes of the values \u200b\u200bthat lie between them, so that the other extreme is excluded. Both the extreme right and the left can be included or excluded.<\/p>\n

It is represented by an expression of the type a \u2264 x or a , which would [a;b)<\/strong>\u00a0\u00f3\u00a0(a;b]<\/strong>.<\/p>\n

For example<\/strong>, if we have the interval semi-open [1;5), tendremos un conjunto de n\u00fameros mayores o iguales a 1 y menores a 5. Incluyendo el 1 pero no el 5.<\/p>\n

\"Representaci\u00f3n<\/p>\n

Representaci\u00f3n en la recta real del intervalo semiabierto [a;b).<\/p>\n<\/div>\n

Intervalo infinito<\/h3>\n

Un intervalo infinito es aquel que tiene un valor infinito en uno o ambos extremos. El extremo que posea el infinito ser\u00e1 un extremo abierto. En caso de que ambos extremos sean infinitos, ser\u00e1 la recta real.<\/p>\n

Se representa con una expresi\u00f3n del tipo a \u2264 x<\/strong> \u00f3 x \u2264 a<\/strong>, lo que ser\u00eda [a;\u221e)<\/strong> \u00f3 (-\u221e;a)<\/strong>. Estos adem\u00e1s pueden contener intervalos cerrados, como [a; \u221e)<\/strong>.<\/p>\n

Por ejemplo<\/strong>, si tenemos el intervalo infinito [1;\u221e), tendremos un conjunto de n\u00fameros mayores o iguales a 1 en adelante.<\/p>\n

\"Representaci\u00f3n<\/p>\n

Representaci\u00f3n en la recta real del intervalo infinito [a;\u221e).<\/p>\n<\/div>\n

Ejemplos de intervalos<\/h2>\n

Para entender mejor el concepto de intervalos, veamos los siguientes ejemplos, junto con su clasificaci\u00f3n y n\u00fameros comprendidos:<\/p>\n\n\n\n\n\n\n\n\n\n
Intervalo<\/th>\nTipo<\/th>\nComprende<\/th>\n<\/tr>\n<\/thead>\n
(-4;6)<\/td>\nAbierto<\/td>\nMayores que -4 y menores que 6.<\/td>\n<\/tr>\n
(16;4)<\/td>\nAbierto<\/td>\nMayores que 16 y menores que 4.<\/td>\n<\/tr>\n
[5;6]<\/td>\nClosed<\/td>\nGreater than or equal to 5 and less than or equal to 6.<\/td>\n<\/tr>\n
[10;14)[10;14)<\/td>\nSemi open<\/td>\nGreater than or equal to 10 and less than 14.<\/td>\n<\/tr>\n
(1; \u221e)<\/td>\nInfinite<\/td>\nGreater than 1 onwards.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n\n
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What are the intervals? An interval is a set of real numbers…<\/p>\n","protected":false},"author":1,"featured_media":426,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-425","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-what-is"],"_links":{"self":[{"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/posts\/425","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/comments?post=425"}],"version-history":[{"count":0,"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/posts\/425\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/media\/426"}],"wp:attachment":[{"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/media?parent=425"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/categories?post=425"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/enorcerna.com\/wiki\/wp-json\/wp\/v2\/tags?post=425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}