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The editor also used these during edit-time, for example, one could WRITE 2 to produce a listing of the code in group 2, or ERASE 4 to delete all of the lines in group 4. [13] Every line must start with a command keyword following the line number. [13] There is no concept of a "default command" as is the case in BASIC with its optional LET ...
August 2024) (Learn how and when to remove this message Type of mathematical expression using basic operations (+, -, ×, ÷, powers, and roots) In mathematics , an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables , and the basic algebraic operations : addition (+), subtraction ...
They may also be performed, in a similar way, on variables, algebraic expressions, [2] and more generally, on elements of algebraic structures, such as groups and fields. [3] An algebraic operation may also be defined more generally as a function from a Cartesian power of a given set to the same set.
To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).
MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral
The simplest example given by Thimbleby of a possible problem when using an immediate-execution calculator is 4 × (−5). As a written formula the value of this is −20 because the minus sign is intended to indicate a negative number, rather than a subtraction, and this is the way that it would be interpreted by a formula calculator.
A substitution is called a ground substitution if it maps all variables of its domain to ground, i.e. variable-free, terms. The substitution instance tσ of a ground substitution is a ground term if all of t ' s variables are in σ ' s domain, i.e. if vars(t) ⊆ dom(σ).
An expectation E on an algebra A of random variables is a normalized, positive linear functional. What this means is that E[k] = k where k is a constant; E[X * X] ≥ 0 for all random variables X; E[X + Y] = E[X] + E[Y] for all random variables X and Y; and; E[kX] = kE[X] if k is a constant. One may generalize this setup, allowing the algebra ...