Suppose we have a field F = {0, 1} 1 + 1 = ? How does one determine if 1+1 = 1 or if 1+1 = 0? Can I define it to be one of the two choices?
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Originally Posted by Noxide Suppose we have a field F = {0, 1} 1 + 1 = ? How does one determine if 1+1 = 1 or if 1+1 = 0? Can I define it to be one of the two choices? There's no choice: it must be that , otherwise we'd get ... Tonio
Ah yes, silly of me to ask. Thanks tonio. 1 + 1 = 1 1 + [1 + (-1)] = 1 + (-1) 1 + 0 = 0 1 = 0
Another way of saying the same thing is that every element of a field must have an additive inverse. The additive inverse of 1 cannot be 0 because . Since 0 and 1 are the only members of the field, 1 must be its own inverse: 1+ 1= 0.