Why will 2 + 2 always equal 4 ?

Of course that is not correct. Whilst it is true that in a decimal system of addition the addition of 2 and 2 makes 4, if you use a ternary base 2 + 2 = 11 and in a quaternary base 2 + 2 = 10.

For those wishing to understand why it is necessary for there to be a restriction on what you can add to 2 in order to achieve 4 in decimal arithmetic you might like to begin by learning the necessary conditions for Ring Theory to be satisfied.

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