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manual:chapter3:reals [2019/11/05 16:32] jojo1973 Added more commands |
manual:chapter3:reals [2019/11/06 15:21] (current) jojo1973 Added Special symbols |
==== Testing ==== | ==== Testing ==== |
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Real numbers form an ordered set and its elements can be compared: **newRPL** provides a full set of arithmetic and logic operators plus some specialized ones. | Real numbers form an ordered field and its elements can be compared: **newRPL** provides a full set of arithmetic and logic operators plus some specialized ones. |
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All these operators (except ''[[manual:chapter6:operators:cmd_ovr_cmp|CMP]]'') return ''1'' __if the test is true__ and ''0'' __if the test is false__. Actually any value different from ''0'' is considered __true__, but conventionally the operators return always ''1'' when the test succeeds. | All these operators (except ''[[manual:chapter6:operators:cmd_ovr_cmp|CMP]]'') return ''1'' __if the test is true__ and ''0'' __if the test is false__. Actually any value different from ''0'' is considered __true__, but conventionally the operators return always ''1'' when the test succeeds. |
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==== Special numbers ==== | ==== Special symbols ==== |
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Operation on real numbers aren't always defined on the whole field of real numbers. | Operations on real numbers aren't always defined on the whole field of real numbers: a notable example is the division, which is not defined if the divisor is ''0''. **newRPL** handles these occurrances defining two special symbols: ''∞'' (//infinity//) and ''NaN'' (//Not-a-Number//). |
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| The ''∞'' symbol is returned when attempting, as anticipated, a division by ''0'' or when the result of a function (e.g. ''[[manual:chapter6:transcendentals:cmd_tan|TAN]]'') diverges. Albeit ''∞'' must not be considered a number, it obeys to a number of rules. The following examples assume flag [[manual:appendix:flags#flag-103|-103]] is cleared. |
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| * ''∞'' ''[[manual:chapter6:operators:cmd_ovr_add|+]]'' or ''[[manual:chapter6:operators:cmd_ovr_sub|-]]'' a finite number yields ''∞''; |
| * ''∞'' ''[[manual:chapter6:operators:cmd_ovr_mul|*]]'' or ''[[manual:chapter6:operators:cmd_ovr_div|/]]'' a finite number yields ''∞''; |
| * the sign rule in multiplication or division applies, therefore ''-∞'' is a valid object; |
| * sum, multiplication or power of ''∞'' with itself yields ''∞''. |
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| The ''NaN'' symbol is **newRPL** way of informing the user that the attempted calculation returns an //undefined// result: typical examples include the calculation of the difference ''∞ - ∞'' or the sine of ''∞''. In general any function that includes ''NaN'' among its arguments will yield ''NaN''. |