why does "2 plus2 equal four" as opposed to "2 +2 equals 5"
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Any one familiar with the Orweillian reference
2+2=4 in a certain universe of discourse
if we allow our universe of discourse to be something like cups of milk and popcorn, we have that 2cups milk+2cups popcorn is not equal to 4 cups of anything.
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perception regulates its confines wouldnt you say
Sure, but if we define the universe of discourse to be such that the above property holds, then we wind up with a lot of useful math. If we have a situation where the above property does not hold, we need be very careful handling it and follow the appropriate rules:
the milk and popcorn thing can be fixed by asking about the total volume taken up by the popcorn (by adding the volume of each kernel) and the volume of the milk. If we work with it that way we can use the addition property we are used to.
In general it is so useful to use the methods the way we are accustomed, there isn't much reason to abandon them unless we have to.