Paola intriguing numbers, which this year will go to primary school, so we tried to explain the first steps.
2 + 1 = 3 is done with what you have on hand: they can be nuts and clementines.
That 2 plus 1 makes 3, it is easy to convince yourself, counting nuts.
Next comes the 3 - 1 = 2: Instead of putting a walnut, is removed. The difficulty of explaining
2-3 = -1, pass through from the nuts (which would require the introduction of anti-nuts, or "credit nuts" ), to scale, but Paul must agree to call "negative" numbers below zero.
Now, of course, "negative" has a negative connotation , and it seems inappropriate to numbers that have not done anything wrong ... but thanks to the boundless confidence that children have in their parents, the rock is exceeded.
I did not go over (I love to Paola), but I tried to imagine what would happen with other, simple steps.
For example, multiplication is easy with the scale: 2 x 3 is made with 2 squares to the right, 3 up, and comes out a rectangle embraced by 6 squares.
Compared to the sum, however, there is a difference, follow me ...
2 nuts more 3 walnuts are a nut, and if we had made 2 nuts + 1 clementine, I know-were-3 results.
If we had 2 nuts + 1 sneeze, would be difficult to say what it does ...
The sum makes sense when we speak of identical objects, or with something in common.
The sum of pure numbers, it is difficult to explain.
Under understood (= hide) refer to what the numbers (like mathematics), is something like a scam. Like those ads that they do everything so you do not understand where's the catch.
In multiplication, the two sides are multiplied on 3 sides, meanwhile, must sit orthogonal (with a common point), then the results are not sides, but squares, that is a "other stuff" ...
You say, one of two things you must read as: "many times" .
true: the multiplication can be viewed in two ways, either as a repetition of a count (count 2, 3 times), or development as a dimension, a dimension orthogonal, but in this case is formed something different from the object multiplied.
The two concepts seem to me very different.
But try to apply the technique of "many times" , with a negative factor ... embarrassing, right?
To make 2 x -3, -3 must take the side of the first zero (we perjury that those numbers were "negative" ). The result is always 6 quardratini, but, apparently, negative ... seem quite similar to those obtained with 2 x 3, but that blessed the unlucky zero.
We try -2 x -3? A
gazzabuglio ...
How do you explain a pure heart, that the product of two negatives is positive ?
Here it takes a lot of imagination , indeed perhaps because of him, "i" , the imaginary number that ago when the square makes them negative.
too much imagination?
But tell me, what is closer to reality: that two negative numbers multiplied together give a positive number, or just the "i" , which, coincidentally, appears in the equations of quantum mechanics ... the kind that so precisely describe the behavior of matter?
But sorry for the digression; in fact the latest intersection between mathematics and physics, is the principle of Universal Preservation. It goes something like this: "for how many elections do, the usual privileges retained their privileges" .
The Anglo-Saxons, who are defining, call them "conservatives" ..
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