CZ:Featured article/Current: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Chunbum Park
(→‎Human rights: set theory)
imported>John Stephenson
(template)
 
(85 intermediate revisions by 5 users not shown)
Line 1: Line 1:
== '''[[Set theory]]''' ==
{{:{{FeaturedArticleTitle}}}}
----
<small>
A '''set''', in [[mathematics]], is a collection of distinct entities, called its elements, considered as a whole. The early study of sets led to a family of [[paradox]]es and apparent contradictions. It therefore became necessary to abandon "naïve" conceptions of sets, and a precise definition that avoids the paradoxes turns out to be a tricky matter. However, some unproblematic examples from naïve set theory will make the concept clearer. These examples will be used throughout this article:
==Footnotes==
 
* A = the set of the numbers 1, 2 and 3.
* B = the set of primary light colors -- red, green and blue.
* C = the empty set (the set with no elements).
* D = the set of all books in the British Library.
* E = the set of all positive integers, 1, 2, 3, 4, and so on.
 
Note that the last of these sets is infinite.
 
A set is the collection of its elements considered as a single, abstract entity. Note that this is different from the elements themselves, and may have different properties. For example, the elements of D are flammable (they are books), but D itself is not flammable, since [[abstract objects]] cannot be burnt.
''[[Set theory|.... (read more)]]''
 
{| class="wikitable collapsible collapsed" style="width: 90%; float: center; margin: 0.5em 1em 0.8em 0px;"
|-
! style="text-align: center;" | &nbsp;[[Set theory|notes]]
|-
|
{{reflist|2}}
{{reflist|2}}
|}
</small>

Latest revision as of 10:19, 11 September 2020

1901 photograph of a stentor (announcer) at the Budapest Telefon Hirmondó.

Telephone newspaper is a general term for the telephone-based news and entertainment services which were introduced beginning in the 1890s, and primarily located in large European cities. These systems were the first example of electronic broadcasting, and offered a wide variety of programming, however, only a relative few were ever established. Although these systems predated the invention of radio, they were supplanted by radio broadcasting stations beginning in the 1920s, primarily because radio signals were able to cover much wider areas with higher quality audio.

History

After the electric telephone was introduced in the mid-1870s, it was mainly used for personal communication. But the idea of distributing entertainment and news appeared soon thereafter, and many early demonstrations included the transmission of musical concerts. In one particularly advanced example, Clément Ader, at the 1881 Paris Electrical Exhibition, prepared a listening room where participants could hear, in stereo, performances from the Paris Grand Opera. Also, in 1888, Edward Bellamy's influential novel Looking Backward: 2000-1887 foresaw the establishment of entertainment transmitted by telephone lines to individual homes.

The scattered demonstrations were eventually followed by the establishment of more organized services, which were generally called Telephone Newspapers, although all of these systems also included entertainment programming. However, the technical capabilities of the time meant that there were limited means for amplifying and transmitting telephone signals over long distances, so listeners had to wear headphones to receive the programs, and service areas were generally limited to a single city. While some of the systems, including the Telefon Hirmondó, built their own one-way transmission lines, others, including the Electrophone, used standard commercial telephone lines, which allowed subscribers to talk to operators in order to select programming. The Telephone Newspapers drew upon a mixture of outside sources for their programs, including local live theaters and church services, whose programs were picked up by special telephone lines, and then retransmitted to the subscribers. Other programs were transmitted directly from the system's own studios. In later years, retransmitted radio programs were added.

During this era telephones were expensive luxury items, so the subscribers tended to be the wealthy elite of society. Financing was normally done by charging fees, including monthly subscriptions for home users, and, in locations such as hotel lobbies, through the use of coin-operated receivers, which provided short periods of listening for a set payment. Some systems also accepted paid advertising.

Footnotes