Why you can't divide by zero? I you for example divide 10 by nothing you get 10

Actually this touches on a more general problem that in k-12 math classes it isn't really touched on that the systems being taught are constructed from axioms which can be discarded or changed. Most people thus have this idea that the math they're taught are the only mathematical systems which exist, which is wrong and borders on intentionally misleading.

>for example divide 10 by nothing you get 10.

Young Grasshopper

We live in primitive times. Our mathematical systems suffer from more inconsistencies than just this.

The dull minds like to think we are at the pinnacle of thought. they can not conceive that we are just beginning along a road of discovery, and as such we are not too far removed from the very first primitives that could think in abstract terms, of assigning a value to an object. The being who first thought of crafting a fish hook stands right next to the likes of Newton, Einstein, along this road.

Consider what we are, a biochemical ordering of impulses, trying to make sense of our existence.

There will be many revolutionary new concepts to be revealed, some lay perhaps millions of years away. But be sure to understand, the day will come when our descendants look back upon these days and consider our perplexities with the likes of zero, the irrationals, the imaginaries, the negatives, and say:

'Oh my god, those fuckwits, man they were dumb'

this is the answer, why is this thread still going on?

Does he still believe 1x1=2?

>Recall from abstract algebra
>implying OP knows shit beyond elementary school math

He can just look it up then - there's no point in me wasting time by retyping out basic definitions.

If 10 / 0 = 10

And 10 / 1 also = 10

Then 10 / 0 = 10 / 1

And that's just fucked up senpai

this.

sage

>And 10 / 1 also = 10
>implying OP is defining things logically

nice grammar you troglodyte

Just think about the definition of division.

If you have 9/3, you get 3 because 9 is divided into equal parts of 3, such that 3+3+3=9.

Now think about 9/0.
Can you divide 9 into equal parts of 0 such that 0+0+0+0.... = 9? No you can not.

This is a terrible definition of definition only suited for primary school children.

>primary school children.
OP said if you divide 10 by nothing you should get 10. I think the explanation is suitable.

How pathetic that that guy would try to think about something in any way other than the most advanced and general possible.

But you're waving it around like it's the actual definition of division - something which can go very wrong for OP if he were to actually take it seriously.

He doesn't need to give it in the most advanced and general way possible, but he should at least give a correct definition.

Where did this come from?

"Split into 0 equal parts" or "split into N number of posts that equal 0"

The logic I explained in highschool was if you put nothing into a box, how long will you spend until the box is full? Forever. Anything/0 is infinity just like anything x1 equals 1.

The teacher denied my claim, and pulled me aside later to explain i was right, but the students needed to be kept in a state of blissful wonder in order for them to feel inspired to explore math, because they assume they're "learning more". Otherwise there's no dopamine realise and the children will not trick themselves into learning, you will have to.

OP's definition overlaps with the definition of division by 1, which fails to be injective

It completely falls apart when you consider anything other than the positive integers, which again, makes it a bad definition for division in any form. Just take the nicer more generalised algebraic definition of left and right inverses, rather than this convoluted one that you've come up with.
It may be intuitive to kids, but it most definitely is not the definition of division.

10 / 1 = 10
1 =! 0
10 / 0 =! 10

Proved your ass wrong OP.

Why would you get ten? If you divided it by 0.1 you'd get a 100.
If you divided it by 0.01 you'd get 1000.

So why the fuck do you think 10 divided by 0 is 10?

I'm currently completing a Masters in Teaching... The truth is, we need to stick to the curriculum, additionally telling students that we 'can' divide by 0 in special cases would blow their minds.

And would also be a complete waste of class time.

zero is not a number like 1, 2, 3 or 10
it has its own personal rules

Let [math] f [/math] be a function defined by [math] \forall x \in \mathbb{R} , [/math] [math] f(x)=1 [/math]
We can also write : [math] \forall x \in \mathbb{R} , [/math] [math] f(x) = \frac {x} {x} [/math] .
[math] f(0)= 1 = \frac{0} {0} [/math]
Therefore, [math] 0 * 0^{-1} = 1 [/math] => 0 has an inverse.

>I'm currently completing a Masters in Teaching.
How does it feel knowing education students are bottom of the barrel university material?

At any rate I don't think having students understand from an early age what math is is a waste of class time; in fact I consider that notion egregiously offensive.

nice circular logic there, bro

The problem is that you CANNOT also write [math]\forall x \in \mathbb{R}, f(x) = \frac{x}{x}[/math] because it's not defined at 0.
There's a stackexchange thread where people talk about the problems with writing it like this and how you interpret it. Anyway, with you trying to use this to say that 0 has an inverse is definitely circular logic as someone has already pointed out.

I think it's absolutely fine to say that "you can't divide by zero" since it's already clear that the universe of discourse is the real numbers.
Imagine if every time you got to an indeterminate form 0/0 (not the same as an undefined form such as 1/0 I know) in real analysis and every time you had to say that we're working in the reals blah blah before applying l'hopital's... it'd just be a waste of time since it's obvious that we're working in the reals.

>I think it's absolutely fine to say that "you can't divide by zero" since it's already clear that the universe of discourse is the real numbers.
I would agree -if- it was made clear that there are other universes of discourse you could consider. It is not, thus I have an issue with this.

It's like having programming be a k-12 subject and the only thing covered that whole time is C; every other language is totally neglected and C is presented as the only programming language.

>C is presented as the only programming language.
In fact even further, C is presented as being literally synonymous with programming.

Do children really think that what is being taught is the be all and end all?
They're taught things such as english and science at school but they know that there are languages other than english and that there is more to science than cells and photosynthesis. Why should they think any differently for maths?

Dividing by zero is infinity.
Ignore everything else.

en.wikipedia.org/wiki/Quotient_space_(linear_algebra)
:^)

>they know that there are languages other than english and that there is more to science than cells and photosynthesis. Why should they think any differently for maths?
Well for one thing we don't call english classes 'language class' and (strictly) biology classes merely 'science class'. That's a bit of a giveaway.
Also helps that most schools teach at least some other languages and a variety of sciences.

>Do children really think that what is being taught is the be all and end all?
Indeed.

Do you think it'd be better to teach children using definitions and examples rather than the way it's being done now?
When they get something wrong we don't need to give convoluted examples of apples and boxes and end up with a Veeky Forums board full of people like the OP and most posters in this thread. Instead, we correct the children by saying that they used the definition wrong (or remembered it incorrectly).
Examples can then be shit like apples and boxes, but not the other way around (where apples and boxes are used as the definition instead).

Have you seen what happens when you divide an atom?!
The closer you get to a real life zero and attempt to divide it the more power is unleashed!

its undefined you knob. from the positive side, the limit approaches infinity. from the negative side, it approaches negative infinity. discontinuous. undefined. lrn2math

There are a few approaches I like but seriously the way we do things now has to be categorically one of the worst you could come up with.

Because there is no number you can multiply 0 with that will equal the top number.

He literally said it in some interview. He also draws "mathematical" diagrams to support his theory. He's pretty fucking retarded.

What does this have to do with it?

lol approaching from the negative side would be dividing by negative zero which is obviously opposite

Lets take f(x) = a/x
Lets take the limit of x as it approaches 0.

As a denominator decreases, but larger than 0, it approaches infinity.

Infinity can be determined as a value outside of all countable numbers. a has no relevance as long as it is a real number.

Thus, and value or expression divided by 0 is indeterminate and thrown out.

what if x/0 is infinity?

Actually you can, they just didn't tell you how.

I will teach you the secret of how to divide by zero:

> 10 / 10 = 1
> 10 / 05 = 2
> 10 / 02 = 5
> 10 / 01 = 10
> ...
> 10 / 0 = infinity

PROBLEM SOLVED, WHERE MY MONIES????

> ...
10 / 005 = 2
10 / 002 = 5
10 / 001 = 10
10 / 0005 = 2
its not working

>10 / 005 = 2
>10 / 002 = 5
>10 / 001 = 10
>10 / 000.5 = 20
> 10 / 00000000.25 = 40
> ..... (notice that the result always increase as it gets closer to zero)
> ... Therefore, the maximum value possible is infinity.
> 10/0 = infinity.

define inverse

It is, its why its "undefined"

0/0 is undefined, 1/0 isn't.

but if infinity is undefined than how can there be different sizes of infinity? how can something without definition, or length, be compared to itself to produce something that also has no length, or definition and be bigger?

why?

you're trolling right?

this you fucking idiots, this

infinity is one word that is used for multiple distinct concepts. those are the different infinities. infinity is not a fucking number.

>infinity is not a fucking number

THAT IS WHAT I HAVE BEEN SAYING THIS WHOLE TIME. FOR FUCK'S SAKE.

>there are different infinities
>it's not a number

WHAT???

How is that not a contradiction? If you can't count it, how can you differentiate between it and anything else? That doesn't make any sense.

nevermind. i'm taking this to sqt

to anyone else, don't reply to my posts

there are no "different infinities", only different perspectives of infinity

Wrong, with counter-proof:
youtube.com/watch?v=lA6hE7NFIK0

the "infinity" contained within differing finite scopes is still infinity. The fact that both 2 and 3 can be divided by 10 doesn't mean that one 10 is bigger than the other

first time on Veeky Forums?

That's liek asking me to divide my pizza pie into 0 slices you airhead

Prove it.

Are you kidding me or just trying to shitpost?
The definition is already there on the fourth line.

The problem here is that you guys haven't defined what an "infinity" is properly. This genuinely is an argument of semantics.

This answer is acceptable ...but really, in its nature, zero isn't a "number", but a "concept". It's like saying, "why can't I divide by green" or "why can't I divide by snorkel".

kek

infinity/0=infinity^infinity=infinity
infinity=!infinity/0

But you still have 10 apples 10/0 =10
Check.
Mate.

Definitions (assumptions) come before conclusions, not after. I'm not sure where you learned to write arguments. It's not my fault I responded to your post thinking you didn't post the definition. Post your definitions before your conclusions next time, my main man.

;)

You probably have adhd if you couldn't read a short post through.
Not sure how you manage to read proofs at all since a lot of them tell the story of what we want before we get there.