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RE: 1 × 0 = 0 BUT 1 ÷ 0 is undefined - school is the rule
Exactly, reality becomes inconvenient at some point for science... If this happens to simple algebra then what about advance physics? If 1 × 0 has an result so should 1 ÷ 0. But not quite, the issue is mixing apples with pears, zero is not a number, zero = the undefined itself.