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If I have a list of 2D coordinates placed in subarrays of a data structure like the following:

testList = Table[RandomReal[{0, 1000}, {RandomInteger[{0, 32}], 2}], {i, 1, 10}];

And if I sneak in a few entries where 2D coordinates have non-real or non-integer component values (positive or negative Infinity values, etc.) is there a way to quickly prune these coordinates away? In other words, I'd like to go through a data structure like testList and quickly delete any coordinate that has a positive to minus Infinity in it.

Is there a way to make something like the following work?:

Select[testList, {_Real, _Real} &];

What if testList is already flattened by one level? Does the larger context of the data structure matter for Select?

The following works for testList, but is not exactly ideal:

For[i = 1, i <= Length[testList], i++,

  testList[[i]] = 
    Select[testList[[i]], NumberQ[#[[1]]] == True && NumberQ[#[[2]]] == True &];

];
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If the list is flattened, you can do:

 Select[testList, #[[1]] \[Element] Reals && #[[2]] \[Element] Reals &]

If it's not flattened, then you can map the select onto the testList:

Select[#, #[[1]] \[Element] Reals && #[[2]] \[Element] Reals &] & /@ testList

For example, if you have terms like {Infinity,Null}, {2,Null}, or {5,-Infinity} in the testList, these terms are rejected.

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