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<blockquote data-quote="fatryan" data-source="post: 2638637" data-attributes="member: 550026"><p>The word <strong>infinity</strong> comes from the <a href="http://en.wikipedia.org/wiki/Latin" target="_blank">Latin</a> <em>infinitas</em> or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end" or "bigger than the biggest thing you can think of") which arise in <a href="http://en.wikipedia.org/wiki/Philosophy" target="_blank">philosophy</a>, <a href="http://en.wikipedia.org/wiki/Mathematics" target="_blank">mathematics</a>, <a href="http://en.wikipedia.org/wiki/Theology" target="_blank">theology</a> and everyday life.</p><p></p><p>In <a href="http://en.wikipedia.org/wiki/Popular_culture" target="_blank">popular usage</a>, infinity is usually thought of as something like "the largest possible number" or "the furthest possible distance" : hence naïve questions such as "what is the next number after infinity?" or "if you travel to infinity, what happens if you then go a bit further?". However, <a href="http://en.wikipedia.org/wiki/Buzz_Lightyear" target="_blank">Buzz Lightyear</a>'s rallying cry ("To infinity — and beyond!"), since it is clearly meant by the filmmakers to be part of Buzz's grandiose delusions and humourously reflect Buzz's limited intellect, actually implies that at least some members of the audience will realise that the concept of "beyond infinity" is ridiculous. However, Buzz's slogan may also be viewed as the rallying cry of <a href="http://en.wikipedia.org/wiki/Set_theory" target="_blank">set theorists</a> considering <a href="http://en.wikipedia.org/wiki/Large_cardinal_property" target="_blank">large cardinals</a>.<a href="http://en.wikipedia.org/wiki/Infinity#endnoteQlarge_cardinals" target="_blank">1</a></p><p></p><p>In <a href="http://en.wikipedia.org/wiki/Mathematics" target="_blank">mathematics</a>, "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things : "an infinite number of terms") but it is clearly a very different type of "number" than the integers or reals. Infinity is relevant to, or the subject matter of, <a href="http://en.wikipedia.org/wiki/Limit_%28mathematics%29" target="_blank">limits</a>, <a href="http://en.wikipedia.org/wiki/Aleph_number" target="_blank">aleph numbers</a>, <a href="http://en.wikipedia.org/wiki/Class_%28set_theory%29" target="_blank">classes</a> in <a href="http://en.wikipedia.org/wiki/Set_theory" target="_blank">set theory</a>, <a href="http://en.wikipedia.org/wiki/Dedekind-infinite_set" target="_blank">Dedekind-infinite sets</a>, <a href="http://en.wikipedia.org/wiki/Large_cardinal" target="_blank">large cardinals</a>, <a href="http://en.wikipedia.org/wiki/Russell%27s_paradox" target="_blank">Russell's paradox</a>, <a href="http://en.wikipedia.org/wiki/Hyperreal_number" target="_blank">hyperreal numbers</a>, <a href="http://en.wikipedia.org/wiki/Projective_geometry" target="_blank">projective geometry</a>, <a href="http://en.wikipedia.org/wiki/Extended_real_number" target="_blank">extended real numbers</a> and the <a href="http://en.wikipedia.org/wiki/Absolute_Infinite" target="_blank">absolute Infinite</a>.</p><p></p><p>In <a href="http://en.wikipedia.org/wiki/Philosophy" target="_blank">philosophy</a>, infinity can be attributed to space and time, as for instance in <a href="http://en.wikipedia.org/wiki/Immanuel_Kant" target="_blank">Kant</a>'s first <a href="http://en.wikipedia.org/wiki/Antinomy" target="_blank">antinomy</a>. In both theology and philosophy, infinity is explored in articles such as <a href="http://en.wikipedia.org/wiki/The_Ultimate" target="_blank">the Ultimate</a>, <a href="http://en.wikipedia.org/wiki/The_Absolute" target="_blank">the Absolute</a>, <a href="http://en.wikipedia.org/wiki/God" target="_blank">God</a>, and <a href="http://en.wikipedia.org/wiki/Zeno%27s_paradoxes" target="_blank">Zeno's paradoxes</a>. In <a href="http://en.wikipedia.org/wiki/Greek_philosophy" target="_blank">Greek philosophy</a>, for example in <a href="http://en.wikipedia.org/wiki/Anaximander" target="_blank">Anaximander</a>, 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass (<a href="http://en.wikipedia.org/wiki/Apeiron" target="_blank">apeiron</a>). In Judeo-Christian <a href="http://en.wikipedia.org/wiki/Theology" target="_blank">theology</a>, for example in the work of <a href="http://en.wikipedia.org/wiki/List_of_Christian_theologians" target="_blank">theologians</a> such as <a href="http://en.wikipedia.org/wiki/Duns_Scotus" target="_blank">Duns Scotus</a>, the infinite nature of <a href="http://en.wikipedia.org/wiki/God" target="_blank">God</a> invokes a sense of being without constraint, rather than a sense of being unlimited in quantity.</p><p></p><p>In a <a href="http://en.wikipedia.org/wiki/Photography" target="_blank">photographic</a> context, infinity is used as the furthest point that a lens can resolve focusing of the subject. This is not exactly true though, as some lens are designed to focus past infinity. These are usually more specialized types of equipment, as now most modern lens types are only designed to focus to infinity. Lenses designed to focus past infinity are mostly used in the scientific field, as these lenses can focus light from the far end of the spectrum beyond visible sight i.e. <a href="http://en.wikipedia.org/wiki/Infrared_photography" target="_blank">infra-red</a>. This light travels at a different wave length to visible light, and as such needs to be focused differently to what we can see with the human eye. Generally these types of lenses will either have a marking on the lens barrel next to the focusing ring, with a red dot or marked with the initials IR, denoting the Infra-Red setting.</p></blockquote><p></p>
[QUOTE="fatryan, post: 2638637, member: 550026"] The word [B]infinity[/B] comes from the [URL="http://en.wikipedia.org/wiki/Latin"]Latin[/URL] [I]infinitas[/I] or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end" or "bigger than the biggest thing you can think of") which arise in [URL="http://en.wikipedia.org/wiki/Philosophy"]philosophy[/URL], [URL="http://en.wikipedia.org/wiki/Mathematics"]mathematics[/URL], [URL="http://en.wikipedia.org/wiki/Theology"]theology[/URL] and everyday life. In [URL="http://en.wikipedia.org/wiki/Popular_culture"]popular usage[/URL], infinity is usually thought of as something like "the largest possible number" or "the furthest possible distance" : hence naïve questions such as "what is the next number after infinity?" or "if you travel to infinity, what happens if you then go a bit further?". However, [URL="http://en.wikipedia.org/wiki/Buzz_Lightyear"]Buzz Lightyear[/URL]'s rallying cry ("To infinity — and beyond!"), since it is clearly meant by the filmmakers to be part of Buzz's grandiose delusions and humourously reflect Buzz's limited intellect, actually implies that at least some members of the audience will realise that the concept of "beyond infinity" is ridiculous. However, Buzz's slogan may also be viewed as the rallying cry of [URL="http://en.wikipedia.org/wiki/Set_theory"]set theorists[/URL] considering [URL="http://en.wikipedia.org/wiki/Large_cardinal_property"]large cardinals[/URL].[URL="http://en.wikipedia.org/wiki/Infinity#endnoteQlarge_cardinals"]1[/URL] In [URL="http://en.wikipedia.org/wiki/Mathematics"]mathematics[/URL], "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things : "an infinite number of terms") but it is clearly a very different type of "number" than the integers or reals. Infinity is relevant to, or the subject matter of, [URL="http://en.wikipedia.org/wiki/Limit_%28mathematics%29"]limits[/URL], [URL="http://en.wikipedia.org/wiki/Aleph_number"]aleph numbers[/URL], [URL="http://en.wikipedia.org/wiki/Class_%28set_theory%29"]classes[/URL] in [URL="http://en.wikipedia.org/wiki/Set_theory"]set theory[/URL], [URL="http://en.wikipedia.org/wiki/Dedekind-infinite_set"]Dedekind-infinite sets[/URL], [URL="http://en.wikipedia.org/wiki/Large_cardinal"]large cardinals[/URL], [URL="http://en.wikipedia.org/wiki/Russell%27s_paradox"]Russell's paradox[/URL], [URL="http://en.wikipedia.org/wiki/Hyperreal_number"]hyperreal numbers[/URL], [URL="http://en.wikipedia.org/wiki/Projective_geometry"]projective geometry[/URL], [URL="http://en.wikipedia.org/wiki/Extended_real_number"]extended real numbers[/URL] and the [URL="http://en.wikipedia.org/wiki/Absolute_Infinite"]absolute Infinite[/URL]. In [URL="http://en.wikipedia.org/wiki/Philosophy"]philosophy[/URL], infinity can be attributed to space and time, as for instance in [URL="http://en.wikipedia.org/wiki/Immanuel_Kant"]Kant[/URL]'s first [URL="http://en.wikipedia.org/wiki/Antinomy"]antinomy[/URL]. In both theology and philosophy, infinity is explored in articles such as [URL="http://en.wikipedia.org/wiki/The_Ultimate"]the Ultimate[/URL], [URL="http://en.wikipedia.org/wiki/The_Absolute"]the Absolute[/URL], [URL="http://en.wikipedia.org/wiki/God"]God[/URL], and [URL="http://en.wikipedia.org/wiki/Zeno%27s_paradoxes"]Zeno's paradoxes[/URL]. In [URL="http://en.wikipedia.org/wiki/Greek_philosophy"]Greek philosophy[/URL], for example in [URL="http://en.wikipedia.org/wiki/Anaximander"]Anaximander[/URL], 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass ([URL="http://en.wikipedia.org/wiki/Apeiron"]apeiron[/URL]). In Judeo-Christian [URL="http://en.wikipedia.org/wiki/Theology"]theology[/URL], for example in the work of [URL="http://en.wikipedia.org/wiki/List_of_Christian_theologians"]theologians[/URL] such as [URL="http://en.wikipedia.org/wiki/Duns_Scotus"]Duns Scotus[/URL], the infinite nature of [URL="http://en.wikipedia.org/wiki/God"]God[/URL] invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. In a [URL="http://en.wikipedia.org/wiki/Photography"]photographic[/URL] context, infinity is used as the furthest point that a lens can resolve focusing of the subject. This is not exactly true though, as some lens are designed to focus past infinity. These are usually more specialized types of equipment, as now most modern lens types are only designed to focus to infinity. Lenses designed to focus past infinity are mostly used in the scientific field, as these lenses can focus light from the far end of the spectrum beyond visible sight i.e. [URL="http://en.wikipedia.org/wiki/Infrared_photography"]infra-red[/URL]. This light travels at a different wave length to visible light, and as such needs to be focused differently to what we can see with the human eye. Generally these types of lenses will either have a marking on the lens barrel next to the focusing ring, with a red dot or marked with the initials IR, denoting the Infra-Red setting. [/QUOTE]
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