how to understand put gamma is always non-negative?

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As the stock price increases, the delta of a (long) put increases from −1 to 0. Gamma is the rate of change of delta with respect to stock price; i.e., it’s the change in delta divided by the change in stock price. They’re both increasing, so both changes are positive; positive divided by positive is positive.

Thanks S2000magician!

My pleasure.