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                      Decimal separator

                      The dot (.) is for the decimal point, the comma (,) is for lists, and the apostrophe ('' ' '') is for derivation. The decimal point is the dot, but the others don't have that function. There is no digit grouping symbol, nor are there spaces. Spaces mean implicit multiplication. The head decimal point is not allowed; use the leading zero in those cases. The trailing decimal point is allowed.

                      Expression Result Expression Result
                      ''3.1416'' OK ''.12'' Error
                      ''3,1416'' Error ''0.12'' OK
                      ''3'1416'' Error ''12.0'' OK
                      ''1 234 567'' Error ''12.'' OK

                      You can convert an exact expression to approximate by making a simple operation with a decimal number, like multiplying by 1.0.

                      Plus Minus

                      Sometimes we are interested in the result of an expression when we add and subtract the same amount, as when we want to compute the roots of a degree two polynomial. The ± symbol allows us such and more things.

                      • If, for instance, we want to compute 3±2, we expect {5,1}
                      • We can also use it as a unary operator: ±2={2,-2}

                      Every possible sign will be computed when we use the ± symbol. Therefore, if we write n± symbols, we will get a list of 2n elements. Some of them may be repeated since it is a list, not a set (for instance, ±0={0,0}).

                      We can use the ± symbol in all the basic operations (plus, minus, product, division, root, power) and some elementary functions (exponential, logarithm, trigonometric and hyperbolic functions and their inverses).

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