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SmartXML, a free programming language with integrated development environment (IDE) for mathematical calculations. Variables of BigNumber type can be used, or regular numbers can be converted to big numbers using conversion operator # (e.g., #2.3^2000.1). SmartXML big numbers can have up to 100,000,000 decimal digits and up to 100,000,000 whole ...
A real number is computable if and only if the set of natural numbers it represents (when written in binary and viewed as a characteristic function) is computable. The set of computable real numbers (as well as every countable, densely ordered subset of computable reals without ends) is order-isomorphic to the set of rational numbers.
Similarly, every cut of reals is identical to the cut produced by a specific real number (which can be identified as the smallest element of the B set). In other words, the number line where every real number is defined as a Dedekind cut of rationals is a complete continuum without any further gaps.
The long real line pastes together ℵ 1 * + ℵ 1 copies of the real line plus a single point (here ℵ 1 * denotes the reversed ordering of ℵ 1) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ 1 in the long real line but not in the real ...
Other early handheld calculators with symbolic algebra capabilities included the Texas Instruments TI-89 series and TI-92 calculator, and the Casio CFX-9970G. [2] The first popular computer algebra systems were muMATH, Reduce, Derive (based on muMATH), and Macsyma; a copyleft version of Macsyma is called Maxima. Reduce became free software in ...
Any real number can be written in the form m × 10 ^ n in many ways: for example, 350 can be written as 3.5 × 10 2 or 35 × 10 1 or 350 × 10 0. In normalized scientific notation (called "standard form" in the United Kingdom), the exponent n is chosen so that the absolute value of m remains at least one but less than ten ( 1 ≤ | m | < 10 ).
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Calculators also have the ability to save numbers into computer memory. Basic calculators usually store only one number at a time; more specific types are able to store many numbers represented in variables. Usually these variables are named ans or ans(0). [3] The variables can also be used for constructing formulas.