Is Tayammum permissible for a sick person absolutely, regardless of the potential harm from water?

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Tayammum is not permissible for a sick person who finds water and does not fear harm from its use. This is analogous to a healthy person who finds water. The basis for this ruling is that the Quranic allowance requires the absence of water, thus not encompassing a situation where water is present but its use is merely optional. Moreover, the allowance requires an implied necessity, and necessity only arises when harm is present.