How can I fix definition gaps? Fixing a definition gap fixable definition gaps
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lernflix.at offers individual online tutoring in mathematics. For more information go to https://lernflix.at/ Mathematically speaking, a sequence of numbers is a mapping that assigns a value in the real numbers to each natural number n. There are a very large number of different sequences, and people are often interested in certain properties such as limit, monotonicity or boundedness. In addition to these criteria, sequences can also be classified according to their formation rule. Sequences with special formation rule: If sequence terms are differentiated by a constant difference, they are called arithmetic sequences. If the sequence terms are differentiated by a constant ratio, they are called geometric sequences. Sequences in which the sequence terms always have a changing sign are called alternating sequences. If a sequence of numbers approaches a certain value g as n increases, this number g is called the limit of the sequence. It is also said that the sequence converges to g. If a sequence has no limit, then it diverges (or is divergent). A sequence with the limit 0 is a zero sequence. Since the partial sums of a series form a sequence, one can also examine possible limits of series. Even if the symbol ±∞ is sometimes referred to as improper limits, they are not numbers and one must not calculate with them. In the mathematical subfield of analysis, a function has gaps in its definition if individual points are excluded from its definition range. This usually involves real, continuous or differentiable functions. The gaps in its definition are the points at which one would have to divide by zero or something similar, for example with rational functions. The gaps in the definition of a function can be classified and, if necessary, "repaired" so that the function can be continued there with the desired properties. In this case, the function can be continued continuously and has gaps in its definition that can be continuously removed. In particular, when a gap in definition cannot be continuously removed, for example because the function tends towards infinity or oscillates very quickly, the gap is also referred to as a singularity, although the language used in these cases is not always consistent. Often, gap in definition and singularity are used as synonyms.
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