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Miloslav Ciz 2023-12-08 15:57:27 +01:00
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infinity.md
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@ -19,4 +19,8 @@ When treated as [cardinality](cardinality.md) (i.e. size of a [set](set.md)), we
**In regards to [programming](programming.md)**: programmers are often just engineers and so simplify the subject of infinity in a way which to a mathematician would seem unacceptable. For example it is often a [good enough](good_enough.md) approximation of infinity to just use an extremely large number value, e.g. the largest one storable in given data type, which of course has its limitations, but in practice [just werks](just_werkd.md) (just watch out for [overflows](overflow.md)). Programmers also often resort to breaking the mathematical rules, e.g. they may accept that *x / 0 = infinity*, *infinity + infinity = infinity* etc. Systems based on [symbolic computation](symbolic_computation.md) may be able to handle infinity with exact mathematical precision. Advanced data types, such as [floating point](float.md), often have a special value for infinity -- IEEE 754 floating point, for example, is capable of representing positive and negative infinity.
WATCH OUT: **infinite universe doesn't imply existence of everything** -- this is a common fallacy to think it does. For example people tend to think that since the decimal expansion of the digits of [pi](pi.md) is infinite and basically "random", there should always exist any finite string of digits somewhere in it; this doesn't follow from the mere fact that the series is infinite (though the conclusion MAY or may not be true, we don't actually know this about pi yet). Imagine for example the infinite series of even numbers -- there are infinitely many numbers in it, but you will never find any odd number there.
WATCH OUT: **infinite universe doesn't imply existence of everything** -- this is a common fallacy to think it does. For example people tend to think that since the decimal expansion of the digits of [pi](pi.md) is infinite and basically "random", there should always exist any finite string of digits somewhere in it; this doesn't follow from the mere fact that the series is infinite (though the conclusion MAY or may not be true, we don't actually know this about pi yet). Imagine for example the infinite series of even numbers -- there are infinitely many numbers in it, but you will never find any odd number there.
## See Also
- [thrembo](thrembo.md)