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GalFisk t1_jedz4kt wrote

Draw him a number line, with 0 in the middle. Show how adding two numbers moves you right, then right again. Show how subtracting two numbers moves you right, then left. Show how adding a negative number moves you left. Then tell him that subtracting a negative number means turning that last operation around once more, meaning you go to the right again. Every minus is a turn.

Edit: if you really want to fry his brain (alternatively inspire him to become a mathematician), tell him that there's also a way to turn away from the number line, and go above or below it.

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gg_wellplait t1_jee36vm wrote

Please fry my brain...how do you turn away from the line???!

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GalFisk t1_jee40gx wrote

With imaginary numbers. They go up and down instead of left and right. If you combine them with real numbers, you get to do math in two dimensions.

I don't know a lot about what it's good for, but I know it has its uses.

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Isolus_ t1_jee7el1 wrote

You could even go two dimensions further and use quaternions...

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GalFisk t1_jee7h79 wrote

Cool, what are those good for?

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Isolus_ t1_jee8pvb wrote

They are often used to describe rotations in the 3D world. So when you have a camera drone (multicopter) there is a good change that they are used to process the sensor inputs (gyroscope/accelerometer) and calculate the corrections needed for a stable flight.

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GalFisk t1_jee92xq wrote

I saw a video on that. They had arrows pointing right, up and front, and connected them end to end in order to make a new arrow that pointed to the destination. Are quaternions the same as making calculations using x, y and z coordinates?

They also used trigonometry to transform back and forth between coordinates and angles.

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Isolus_ t1_jeeeqwy wrote

There are different ways to achieve this and it's hard to say what you have seen. The "classical" and "easy" approach is to use vectors and apply rotation matrices. But for a flying device you often rotate around an arbitrary axis and not around x, y or z. That is where quarternions come in handy. They can represent a rotation around an arbitrary vector. But they are harder to understand so most teaching of those concepts is done the "classical" way. Quaternions are also numerically stable. Computers can only represent an approximation of a number (for example you can't store Pi, only the beginning). Using matrices it's happens more easily that an error introduced through these approximations changes your result a lot.

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EveningSea7378 t1_jee3178 wrote

> tell him that there's also a way to turn away from the number line, and go above or below it.

Only if you totaly change the deffinition of what your numberline is on the way. You can not find i in the natural numbers.

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mikeholczer t1_jee64gg wrote

The same can be said about negative numbers or real numbers.

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Menolith t1_jedz7pv wrote

It helps to think of the sign as a direction. Above zero/below zero, credit/debit, above sea level/below sea level, etc. When the sign changes, you change direction.

So, +1 is "take a step," and -1 is "turn around and take a step" which means you move backwards one step.

With --1, you're essentially saying "turn around, then turn around, then take a step," which results in you just spinning about and moving forward just like with +1.

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Dreamwalk3r t1_jedzapo wrote

Let's say your son has -1$. Imagine it as he owning that dollar to you. If you multiply that debt by 2, the debt is now 2 dollars. If you multiply it by zero, the debt is now cancelled. If you multiply it by -2 the debt turns to credit and now he has 2 dollars.

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MidnightAdventurer t1_jee0dab wrote

Think of the minus as taking something away and addition as giving something back. If you take something away from the things that are going to be taken away then it is effectively being given back. This is what the double negative is representing

For example:

You have $10 and owe your friend $6 so now you have $4 left. Now, lets say that your friend decides that he'll forgive $2 from the debt. So, the debt is now $4 (6-2 =4).

You can now subtract $4 from $10 and have $6 left over but you can also do this as a single equation:

10 - (6 -2) = 6

The brackets are clarifying it but we don't really need them - you can write it as

10 - 6 - -2 = 6

To summarise: You have $10 (+10), you owe $6 (-6) minus the $2 (--2 = +2) you were forgiven so you have $6 left after you pay your friend back

You can also do this with physical objects as a practical demonstration.

Make a pile of blocks, take some away then take some out of the pile that is being taken away and give them back. The ones you take away are the single negative, the ones you give back again are the double negative

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therealdilbert t1_jee6lmu wrote

take a step forward , that's plus one
take a step backwards, that's minus one

take a step backwards but do it in reverse, that is minus minus one = plus one

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homeboi808 t1_jee15d5 wrote

You can think of - like “opposite of add”.

If you owe me $1, you have now -$1 compared to before.

If I do the opposite, now I give you $1 and now you have +$1 compared to before.

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SifTheAbyss t1_jee3x3g wrote

Multiplying with negative is just turning around the direction of whatever you're doing.

Using the classic fruit example, adding gives you more apples, adding "negative apples" takes away apples. You can draw a card that says "you need to hand over 1 apple".

Now, adding 1 of these cards really just removes 1 apple. It's like a negative apple.

What happens if we remove 1 of these cards? You have 1 more apple than you had before.

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TheBarghest7590 t1_jeeaydy wrote

My maths teacher used a rather helpful little memorable explanation for my class (honestly that guy was a fucking legend, wish I had the time to pop into my old school for a quick visit with some of those teachers, some really are damn fine at their jobs)

See the positives and negatives as cowboys. It’s a silly thing but it’s the silly stuff that sticks in your head far easier and longer. For below, take a to mean a cowboy and b to mean a town.

A good cowboy visiting town is good: a + + b = positive (or just a + b)

A good cowboy leaving town is bad: a + - b= negative (or just a - b)

A bad cowboy visiting town is also bad: -a + b = negative (shown as a - + b)

But, a bad cowboy leaving town is good: -a - b = positive (shown as a - - b)

Now I’m not a teacher (don’t envy their job at all) and it has been… let’s just say quite a few years since I was at school and leave it at that… if I’ve not explained it clearly then my apologies, but that should hopefully be useful. It’s also good to see positives and negatives as literal mirrors of each other. Zero is the mirror line, but they are the exact same and work the same way… so remove the positive and negative prefixes, you’ve just got numbers… and adding and subtracting then becomes trivial. The + and - complicate the look of it… but ultimately the numbers behave the same regardless if they’re positive or negative so they only way to make add and subtract behave in the exact opposite way to what they typically do… is to use numbers from the opposite side of that mirror line. Otherwise add will always go up, and subtract will always go down…

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