Zero to the power of infinity

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As you would probably expect

Any number multiplied by 0 remains zero. Because

0 × 7 = 0 and 0 × 0 = 0

but we know also that

0 × ∞ =?

It can have any value. Well, infinity is not a number. But what about

Here you multiply zero with other zeroes infinitely many times. You do not multiply it with infinity. So it stays