What's 9 + 10?

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21

9+10 is obviously 109 on sunny days, and 910 on rainy days.

It may also be whatever you want on your cakeday, like 21.

Here's why :

For each integer ** n**, its square is defined as :

`n² = n + n + n + ... + n`

(example :

`9² = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9`

The derivative of

`n²`

`2n`

`n`

`1`

Then, the derivative of the square equality above is :

`2n = 1 + 1 + 1 + .... + 1`

But... but... but... but the sum of n times 1 is n, thus

`2n = n`

If

`n = 1`

`2 = 1`

By removing the equal symbol, we get

`21`

`9 + 10 = 21`

(already tried to explain that to my banker, no luck so far, any help appreciated... lol)

2 weeks ago

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I *really* like your explanation, even though it's so easily proven wrong. Have a whitelist for excellence in weird math.

For each integer n, its derivative is 0, and the derivative of its square n² is also 0, because both are constants, and the derivative of a constant is zero.

2 weeks ago

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Thanks for the 💙

But... but... but... but if the the derivative of a constant is zero, then we have :

Let our square function be `f(x) = x³`

Its derivative is ** f’(x) = 2x** (by definition)

Then for every

`x`

`x`

`x²`

`x`

`f’(x) = 0`

`x`

Thus

`2x = 0`

`x`

But this cannot be true because I already showed that

`9 + 10 = 21`

😂😜

2 weeks ago

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I have! By accident. My code crashed. :(

I mean, technically, we *can* divide by zero; the result is infinity. The problem is that this breaks all finite numbers, because now you have infinity and finite numbers can't play ball anymore, so we just learn in school that we can't; it's one of the lies-to-children the learning process relies so heavily on. And implementing proper handling of infinity on computers is hard, to say nothing of pocket calculators, so the process feeds upon itself.

What you *actually can't* do is one of the handful of truly undefined operations, such as dividing zero by zero; even so, you can calculate the limit of such an operation as the numbers approach the undefined point. For example, sin(0) = 0, and sin(0)/0 = 1, because even though 0/0 is undefined, you can calculate the limit of sin(x)/x as x->0, and you will find that the result of that operation is cos(x), and cos(0) = 1.

But the Real Truth™ of the matter is that this is the best kind of way to interpret division by zero:

2 weeks ago

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Well, all of this is really tricky, but you're close to the answer, after a small circumvolution 🤔

Yes, the limit of ** f(x) = a / x** with

`a ≠ 0`

`x ↦ ±0`

`±∞`

`∞`

`ℝ`

`ℵ0`

`ℕ`

To my eyes it's not a real Lie-to-children because most children (except genius ones) precisely expect that the result of any arithmetic calculation is a number in its ordinal meaning (after all that's how the idea of what is a number is taught). The lie would be to show them the

`∞`

About mathematically computing ** 0 / 0**, this trigonometric trick is known, but... a graphical representation easily shows that

`sin(x) / x`

`cos(x)`

`x ↦ ±0`

But the similarities stop there, even if

`sin(0) = 0`

`x ↦ ±0`

`x ↦ ±0`

`a ↦ ±0`

`x ↦ ±0`

Anyway, if you ask a physician about ** 0 / 0**, they may answer you that

`0 / 0`

2 weeks ago

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No, no, not at all. Mostly memories from high school. Here in France all of this should be understandable by pupils in last year of high school, if they choose to specialize in maths (not the majority, by a fair amount). When I write "should be understandable" I mean it's right above what is expected from the students but not complicated enough to be beyond their reach when compared to what is taught.

There you go for the official teaching program in French high schools (for the last year, with specialization)... ( source ) It did changed a little when compared to my era (ahem), but not much.

But yes, I went higher for my studies, so maybe... *maybe* I'm mastering it a little more than back when I was in high school 👨🎓 (but not that much).

2 weeks ago

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*brings up that old rusty French knowledge from back whenever and tries to read*

Ehhhh... Wow, you really go pretty far in math, when you choose to. There's even stuff I'm fairly sure I never studied, and that's considering I have an engineering degree (it wasn't necessary for engineering and we have only so much time). There's a ** lot** of stuff that we don't see in high school in Brazil. That really drives home just how bad our school system is. :(

Perhaps the issue at hand is that, at high school, we have more leeway to get into the whys and hows of things, whereas in higher education we have a lot of stuff to burn through and much stronger time constraints. So you had the leeway to look and understand more deeply, whereas we had to simply learn the motions and the barest minimum of the rules so that we wouldn't do the wrong thing. Not sure, though; it's just a possibility.

2 weeks ago

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Most students here do not choose this specialization, often seen as the hardest one (to get the diploma, it costs more negative points when you fail at it than others specializations), and others can be more interesting, but are not available in each school. Engineers here are not necessarily better than you, there's no need to follow that path to enter engineering schools.

Not sure your school system is bad, all of this stuff is mainly funny tricks you'll never stumble upon during a normal life, but understanding those correctly helps me to understand what is a limit, what is a set, what is "dividing" : that's easier for me to remember those tricks than to remember the "normal", very boring, definitions of things ;) Aaaannnnd, you know, seeing someone good at one thing doesn't mean he's good at any other thing ;) lol

I'm just curious, that's why I go to those extents... Last time I had a serious and difficult and real math problem to deal with, it was about implementing programmatically a way to do 3D rotations to move virtual objects in 3D, with either matrices or quaternions. I never studied that, but succeeded in using quaternions, and ... it didn't solved my problem completely, but not because of my maths at least ! (the coordinates I had to deal with were somewhat "twisted" in a regular way, and I hadn't enough time to investigate and write code about that).

Well, by comparison, thinking about dividing zero by zero make me feel more restful ! 🤣

1 week ago

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Well, yeah, math tricks *are* fun. Especially when you very subtly break a rule in order to "prove" something obviously false (such as 0=1). People are nearly always baffled by it. :D

And I'm pretty sure I *am* a bad engineer, not because our school system is bad (that's a different issue), but because I chose to work with something else despite my diploma exactly because I don't trust myself to not kill people due to sheer incompetence. Or maybe the feeling that you're incompetent is normal and I just went full paranoid; I don't know.

1 week ago

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Not an engineer myself, I can't really tell you. First time I had to design something to kill people, I was 6 and it was all about choosing the right tree branch to make a bow. Arrows were not firing straight... But I didn't gave up (hence my profile background).

😂

But, seriously, working with the right or wrong people can have a huge effect on how one feels at work... (just my 2 cents)

1 week ago

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Now I have to crumple up my previous work and throw it in the *bin*

Base 19 and Base 21 is the answer! They equal!

2 weeks ago

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Today's 9/10/21...

I've asked this question before, but today is my cakeday. So please, as this day might be the last chance to ask, and get a final answer. What is 9+10?

Is it 19?

Or is it 21?

And if you want to meet in the

middleof the road... nO. 😒Off the topic, but some people think that your birthday/cakeday is the day you should receive stuff. However, when I was in elementary school, it was customary to bring some sweets to share with the class to compensate them for singing Happy Birthday song. I believe something similar is going on here on SG.

So enjoy your treats :P

And while we're talking about treats, I want to recommend you a book. It has 5 letter title...

Can you guess it? :3

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