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Worse than that, it could be bounded above. If your day's value is 1 - 1 / n (where n is the number of the day in your life) then every day is above the average of the previous days (since bigger than the largest, yesterday) but will never be bigger than 1.

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Thanks, that's about what I suspected right after posting ('something like log-function'). But does it have to be?

The more I think about it, there's quite a wide range of data sets I can create from my initial rule. The daily increase is not limited, so it should be possible to create almost every kind of graph, as long as it increases. Truely a noob question I came up with, if I don't overlook something again...

It could be even constant except for day 0. value = 0 for day 0, value=1 for all other days.

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