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| | Hi there. Allow me begin by introducing the writer, her name is Sophia. What I [http://hknews.classicmall.com.hk/groups/some-simple-tips-for-personal-development-progress/ psychic love readings] performing is soccer but I don't have the time recently. Office supervising is what she does for a residing. Kentucky is exactly where I've always been living. |
| {{Portal:Mathematics/Feature article|img=|img-cap=|img-cred=|more=Continuum hypothesis|desc=The '''continuum hypothesis''' is a [[hypothesis]], advanced by [[Georg Cantor]], about the possible sizes of [[infinite set]]s. Cantor introduced the concept of [[cardinal number|cardinality]] to compare the sizes of infinite sets, and he showed that the set of [[integer]]s is strictly smaller than the set of [[real number]]s. The continuum hypothesis states the following:
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| :There is no set whose size is strictly between that of the integers and that of the real numbers.
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| Or mathematically speaking, noting that the [[Cardinal number|cardinality]] for the integers <math>|\mathbb{Z}|</math> is <math>\aleph_0</math> ("[[aleph number|aleph-null]]") and the [[cardinality of the real numbers]] <math>|\mathbb{R}|</math> is <math>2^{\aleph_0}</math>, the continuum hypothesis says
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| :<math>\nexists \mathbb{A}: \aleph_0 < |\mathbb{A}| < 2^{\aleph_0}.</math>
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| This is equivalent to:
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| :<math>2^{\aleph_0} = \aleph_1</math>
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| The real numbers have also been called [[Real line|''the continuum'']], hence the name.|class={{{class}}}}}
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Latest revision as of 19:45, 5 September 2014
Hi there. Allow me begin by introducing the writer, her name is Sophia. What I psychic love readings performing is soccer but I don't have the time recently. Office supervising is what she does for a residing. Kentucky is exactly where I've always been living.