# A word for a {[x1, y1], [x2, y2], .... } collection of data where x is strictly progressive

You can see those everywhere, any kinds of statistics like average temperature by month or average income by years of education, essentially any data that is a list of progressive x values corresponding to y values. Example: There are a few words that I know that would fit this data, for example "polygon" and "graph" but that is like calling a cat an animal - technically correct but not very specific. Polygons and graphs have no restrictions on whether any of their dimensions are progressive or even how many other data nodes a single node is connected to.

Then there is "chart" but AFAIK this word refers to a visual representation of some data and is even more vague.

Does anybody know of a word that would fit only this sort of data specifically?

• History? Timeline? These only work for time-related progressivity. Are you thinking about a broader definition of progressivity? ANd if so, what kinds of examples do you have that aren't time-related? Jan 2, 2017 at 4:56
• As CandiedOrange’s answer implies, you're looking at this backwards. The progressiveness of the X value is not a property of the data set itself, but of how it is sorted. A set of data has no inherent sorting, and as long as the X-Y pairs aren't messed up, it remains the same data set even if you shuffle the entries randomly. Jan 2, 2017 at 5:18
• Isn’t this just called a dataset?
– Jim
Jan 2, 2017 at 5:21
• You use set notation, and the members of a set are not necessarily ordered. Probably you mean for them to be ordered by the first members of the ordered pairs, in which case you have a sequence of ordered pairs. Jan 2, 2017 at 5:43
• "Time-series", perhaps?
– Mick
Jan 2, 2017 at 7:34

The restriction that X be strictly progressive is slightly odd. The data is the same regardless of how the data is sorted. If I can assume that to mean that X values won't repeat I have a name:

Function

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

If your data consist of values across time, the term you're looking for is time series. Often the data points occur at equally spaced intervals, but not necessarily.

This idea is called a monotonicity, but the usage in mathematics is highly ideomatic. As the commenters have pointed out, most functions are understood, if not outright defined this way (the idea is inherent in the idea of an independent variable). So the term monotonic is almost always applied to the dependent variable, not the independent variable.

2 : having the property either of never increasing or of never decreasing as the values of the independent variable or the subscripts of the terms increase

"Monotonic." Merriam-Webster.com. Merriam-Webster, n.d. Web. 5 Jan. 2017.

• Monotonicity is something I thought of too; however, I didn't propose it exactly for the reason you mentioned about it being applicable to the dependent variable. The OP mentioned about x being progressive, not y (the dependent variable). In fact, in the example graph, y is not monotonic. Jan 5, 2017 at 7:10

As mentioned by Phil Sweet in another answer, the idea of progressive values (monotonicity, if we can say so) of x is usually implicit because it is inherent for the independent variable; irrespective of which order of x the data is presented in, it is invariably sorted by x for any further analysis or charting.
With that context, for each data point, you are asking for x to be distinct (meaning each value of x appears only once in the dataset which rules out a polygon), so that kind of data represents a single-valued(one-valued) function.

TFD(encyclopedia):

single-valued function (mathematics)
A function for which exactly one point in the range corresponds to each point in the domain; a function that associates to each value of the independent variable exactly one value of the dependent variable. Also known as one-valued function.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

If the independent axis (x-axis) is increasing by fixed time increments, then it is called a Time Series.

A time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.

Econometrics has an entire specialty devoted to Time Series, which is taught through graduate classes like this one, called "Cross-section and Time Series Econometrics (ECON6113)."