What’s so special about Cauchy sequences? This makes them very well suited to model real world processes. The good thing about Cauchy sequences is that they have some interesting properties.
We can see that the values are getting close to each other as the wave progresses. We can see that the values are not getting close to each other.
DEFINITION OF CAUCHY SEQUENCE SERIES
Going by this definition, the elements of the harmonic series wouldn’t form a Cauchy sequence.įor example, consider the following figure of a sine wave: It’s important that all the elements of the sequence after a particular point become close to each other.
An important thing to note is that it’s not sufficient a given element gets closer to the preceding element. Let’s dig deeper and see why it’s relevant, shall we?Ī Cauchy sequence is a sequence whose terms become arbitrarily close to each other as it progresses. Cauchy sequence is one such sequence that’s very fundamental to a lot of fields. This allows us to approximate real world processes using these sequences so that we can estimate what’s going to happen in the future. In theory, we can design sequences with amazing characteristics and study them. If we look closely, we can see that sequences are rich in information. Repetitions are allowed in this case, which means any element can reappear in a given sequence. A sequence is a collection of elements where each element is indexed. Some of the examples include sensor data, stock market quotes, speech signals, and many more. Sequences occur everywhere in our daily life.
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