Why minus times minus gives plus?
The confusion of the minus-operation and the minus-state in the meaning of the word “minus”.
If the father is a swan and the mother is a swan, the child will be a swan.
If the father is a duck and the mother is a swan, the child will be a duck.
If the father is a swan and the mother is a duck, the child will be a duck.
Why, if the father is a duck and the mother is a duck, the child will be a swan?
The answer will be very simple to the question; “In the field of the real numbers, why a multiplication of minus times minus gives plus?”
In everyday life, the word “minus” has two distinct meanings.
· Such as on a thermometer, the absolute “minus-state”, which is smaller than 0.
− |a| < 0 , a ≠ 0
· The “minus-operation”, which changes a minus sign into a plus sign, or changes a plus sign into a minus sign. The plus sign is not written. The minus-operation is not an operation to make a minus-state.
− → +
+ → −
The minus-state is a minus-operation onto an absolute value, so the only function of the minus sign is minus-operation. The minus-operation is a definition of operation, and there is no proof regarding the minus-operation.
The question; “why minus multiplied by minus gives plus?”, that is an erroneous quetion; “Why a minus-state multiplied by a minus-state gives a plus-state?”
Why, if the father is a duck and the mother is a duck, the child will be a swan?
Illusion of the minus-state
You can say to the calculator; “this minus sign, it means a state of debt,” but the calculator has no ears to hear your words. The minus-state is used, for example, for thermometers, etc., but the minus-state does not exist in the calculation expressions. The signs, ＋－× ÷ , are signs of calculation operations, in algebra, these signs do not have the ability to express states of things or meaning of things. The function of the minus sign is only the minus-operation, and the minus sign cannot express a thing missing, one thing that has been removed, a debt, a negative number, a duck. The subjective idea of a minus-state of the person who is doing the calculation cannot be represented by a minus sign on the paper. A minus sign does not represent any picture.
For example, the person who does the calculation has the right to imagine in his head a line segment in a minus-state which has a length of －3, but on the paper, only a minus sign is placed next to a number. The image of the minus-state of a negative number is only in the head of the person who is doing that calculation.
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The confusion of the minus-operation and the minus-state in the meaning of the word “minus”.
A protected expression.