issue about ismember wrong output

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jason lee
jason lee 2020 年 3 月 24 日
編集済み: Stephen23 2020 年 3 月 24 日
a=0.02:0.02:2;
b=0:0.01:5;
ismember(a(6),b)
ans =
logical
0
But it is clear that all elements in a belong to b, so where is the problem?

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Walter Roberson
Walter Roberson 2020 年 3 月 24 日
You forgot that in binary floating point representation there is no exact equivalent to 0.1 or 0.01 or 0.02, only approximations of those. When you add up those approximations of 0.01 you are not necessarily going to get exactly an approximation of 0.02 especially since you start the 0.02 accumulation at a different start point.
Consider the analogy in decimal of 1/3 to two decimal places. 1/3 decimal is 0.33333333 with the 3 infinitely repeated. To two decimals, 0.33. Now add another of the same to that and you get 0.66. Is that the same as the 2 decimal approximation of 2/3? No, the 2 decimal approximation of 2/3 is 0.67. This illustrates that when you add up truncated approximations that you do not necessarily get the same as the direct value.
The moral of the story is to avoid exact comparisons in floating point. See ismembertol
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Walter Roberson
Walter Roberson 2020 年 3 月 24 日
The .9 repeated == 1 is however only true for infinite precision. If you were to stop at 10^43 decimal places, then you would indeed have a value mathematically less than one.
Physically, if you were to stop at 1e-43 metres, it is unclear what the result would be. There have been serious proposals that space as we know it does not exist below about that small, that everything is a quantum foam.

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