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we know in uniswap v3 the tick range is [−887272,887272]. My question is, is this for each price range or total of all price ranges should be in this tick range??

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Tick index range is [-887272, 887272]. This covers the entire price ranges.

With the base 1.0001, powering it to the tick index i from -887272 to +887272 gives you a huge range:

>>> # python 3.11 shell
>>> import math
>>> math.pow(1.0001, -887272)
2.938956807614301e-39
>>> math.pow(1.0001, 887272)
3.4025678683306347e+38

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