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/sci/ - Science & Math

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9728694 No.9728694 [Reply] [Original]

I teach math in a middle school. I put "Write a fraction that is not a rational number," on a test and a kid wrote "1/0".

So is he right or not?

>> No.9728696

ask your teacher brainloid

>> No.9728697

>>9728696
But I am the teacher.

>> No.9728704

>>9728694
>write a fraction that is not a rational number
You were hoping for an infinite continued fraction?

>> No.9728706

>>9728704
I was hoping for Pi / 2.
Basically just a fraction with anything other than integers in it.

>> No.9728710

>>9728694
He's wrong, if you are a middle school teacher you should know that.

>> No.9728719

>>9728710
I was thinking about number systems where division by 0 is possible and also the possibility that a fraction which is undefined in this number system is still a fraction but I think I was thinking too much on it. Wrong it is then.

>> No.9728720

>>9728694
He is wrong, a fraction needs to have a non-zero denominator.

>> No.9728730

>>9728720
https://en.wikipedia.org/wiki/Division_by_zero

>> No.9728734

>>9728706

0^-1 is not a number wtf anon

next time put on the test "write a fraction with a non-rational number in the numerator"

>> No.9728748

>>9728734
It's not a real number, but it is a number in another number system but I will still mark it wrong. The class is outside of the US and the students are all ESL so sentences have to be concise and basically only use specific vocabulary they know but I see and will do it differently next time.

>> No.9728772

>>9728730
https://en.wikipedia.org/wiki/Fraction_(mathematics)

>> No.9728774

>>9728706
Why? A non-constant rational function with integer coefficients would be fine too, it's not a rational number

>> No.9728782

>>9728774
Agreed. That would have been fine too.

>> No.9728787

>>9728719
Have you heard of z-numbers. You let z^1(1) = 1/0, z^2(1) = 1/0^2,
\dotsc. These constitute a well defined algebraic object, with inverses of multiples of zero, so you also have to do z^{-1}(1) = 0\cdot 1, \dotsc. You then add as \sum_[i \in integers] z^i a_i + \sum_[i \in \integers] z^i b_i = \sum_[i \in \integers] z^i(a_i + b_i) and multiply by the convolution product.

>> No.9728813

>>9728694
[math] \frac{1}{0} [/math] is not a number (in [math]
\mathbb{R} [/math] ). therefore it is also not a rational number. It is a ratio of two numbers though so it is a fraction. Therefore he is right.

>> No.9728888

>>9728813
[math]\frac{1+0i}{0+0i}[/math] isn't valid in complex numbers either iirc

>> No.9728905

>>9728888
Regardless of that, the kid is still right.

>> No.9728927

>>9728694
Given the ambiguity of what you wrote, give him credit. Next time make it clear that it has to be irrational but not rational.

>> No.9728992

>>9728905
well yeah, it's definitely not in rationals, but it isn't a valid fraction either.
Should it count? sure. It respects the fact that the fraction itself isn't in [math]\mathbb{Q}[/math] and it also isn't in [math]\mathbb{C}[/math]
If you wanted them to write fractions that are in [math]\mathbb{R}[/math] but not in [math]\mathbb{Q}[/math] you should have specified it

>> No.9729053

>>9728694
>irrational fraction

Or in other words, not a fraction.

>> No.9729184

>>9728694
>a fraction
Is there any mathematical definition for the word "fraction", if not I would define it as "one number divided by another number", in that case his answer is right, he wrote a fraction which wasn't a number, especially not a real number.

>> No.9729482

>>9728813
Of course it's not rational, however it isn't irrational either. Kid's wrong and it's only because he has a shitty teacher who doesn't bother with defining what he teaches.

>> No.9729491

>>9728694
You fucking moron, every fraction is rational.

>> No.9729503

>>9729491
Ahahha

>> No.9729562

>>9729053
You clearly don't know what either of those words mean.

>> No.9729566

>>9729491
Objectively wrong. Only simple fractions are rational.
1/Pi

>> No.9729568

>>9728694
Yes he's right.

Why are you asking this question? Shouldn't you have the skill to understand definitions and reason logically? The absolute state of middle school teachers

>> No.9729569

>>9729568
He could of drawn a pizza and have been right with that logic.

>> No.9729573

>>9729569
Wrong, but his teacher would have deserved that answer for writing such a stupid question.

>> No.9729580

>>9729573
He clearly stated in previous posts he wanted an answer that was irrational. If he wanted answers that weren't even real numbers children could put any idiotic answer they so desired.

>> No.9729582

>>9729491
No, every fraction a/b where a and b are integers and b is not 0 is rational

>> No.9729583

>>9729580
He wanted a fraction. A pizza isn't a fraction you fucking idiot

>> No.9729590

>>9729580
So are kids supposed to guess what their dumbshit teacher wanted instead of what's written?

>> No.9729603

>>9729590
They should obviously be able to take information from what they learned and have applied those concepts to solve problems. It's obvious the teacher is shit at his job. That fact doesn't make the kid right.
>>9729583
1/0 is not a fraction either it's undefined.

>> No.9729613

>>9728694
The kid found, probably inadvertently, a loophole in the description you taught. I'd give it to him, cause it seems pretty cool. Then you can just explain how you can make a fraction that's irrational and make a fraction that's not a number or something.

>> No.9729637

>>9729482
So [math] \frac{i}{2} [/math] would be wrong in your opinion?

>> No.9729652

>>9729482
He wasn't asked to write down an irrational number you fucking retard.

>> No.9729654

>>9729603
Yes, it's an undefined FRACTION

>> No.9729689

>>9728694
He's right, and you know it

>> No.9729694

>>9728927
Mark it wrong. Its implied that the class is working with real numbers.

>> No.9729783

>>9729053
Irrational isn't defined as not being expressible as a fraction, it's defined as not being expressible as a ratio of 2 INTEGERS brainlet.

>> No.9730877

Its not a fraction jesus, the bottom number not being 0 is part of the fucking definition of a fraction.

>> No.9731709

>>9728694
what the fuck kind of question is that.
A rational number is a number that can be expressed in a ratio, hence the name.
An irrational number is one that cannot be expressed that way. That is, a number that can't be expressed as a fraction of two integers.
only answer would be writing a fraction with pi, e, sqrt(2), or other irrational numbers as denominators and numerators. even that is just stupid, as the fraction of two irrationals could very well be a rational number (proof needed for the contrary).
learn to teach you asshole, you could pretty much ask the kid to lick his own elbow.
you asked a stupid question, got a stupid answer.
>>9728706
also, proof needed for that too

try instead to ask them to identify rationals and irrationals in a list of different numbers. Or just simply explain why a rational is called rational.
think about what kind of thought you are trying to inspire when making questions.
source: math teacher myself

>> No.9731713

>>9728694
Teacher in what country, anon?

>>9729569
It really depends on what fraction of the pizza was eaten already.

>> No.9731715

But, is, say, pi/1 really a fraction?

>> No.9731753

i think he's wrong.
to me a fraction is an expression of the form [math] \frac{p}{q} [/math], where [math] p,q\in\mathbb{C} [/math] and [math] q\neq0 [/math].
there is no reason why you should want or expect the definition to include expressions with [math] q =0 [/math] anymore than you should want expressions like [math] \frac{\begin{pmatrix}1&2\\ 5&2\end{pmatrix}}{\begin{pmatrix}7&2\\ 1&3\end{pmatrix}} [/math] included.
on the other hand, you can only mark him on what [math] you've [/math] taught. if you've defined a fraction another way (or not defined fractions at all), then he should get partial credit at least

>> No.9731838

>>9728787
interesting, any reading i could do on them other than a simple google search?

>> No.9731868

>>9728694
Give him half a point, and explain that while 1/0 is not a rational number, it is not a fraction.

>> No.9731879
File: 98 KB, 960x960, 1474941098723.jpg [View same] [iqdb] [saucenao] [google]
9731879

>>9728706
>let A be a circle with diameter d>0, d∈R
>Define the circumference of circle A as C, c∈R
>Ans: c/d

>> No.9732015

>>9731709
That's not what rational means, retard. See >>9729783

>> No.9732049

he's right, next time word your questions more carefully

>> No.9732071

>>9728694
They're right, it is a fraction and it is not a number (so it is not an irrational number).

>> No.9732072

>>9731753
A fraction is just notation, not necessarily a number. In intro calculus you often have to deal with fractions where the denominator is equal to 0.

>> No.9732211

>>9728694
Ask him if he can explain a situation where 1/0 actually makes sense.

If he can, give him credit. If not, don't.

>> No.9732213
File: 58 KB, 679x769, 1512561926628.png [View same] [iqdb] [saucenao] [google]
9732213

>>9732072

>> No.9732252

>>9732072
>A fraction is just notation
a fraction has notation to denote it, but is not itself a notation.
the notation of a fraction refers to the placement of some symbol (/ or — or other) upon/about two numbers to represent division. a fraction itself is what i described before.

maybe you should finish that intro calc course before posting here again.

>> No.9732266

>>9728694
>So is he right or not?
it depends solely on your definition of "fraction". what is your definition of "fracion" ?

>> No.9732331

>>9732213
>>9732252
A fraction is notation that extends the multiplicative notation used for groups. Ideally you probably want it to be abelian but you can probably still use it for bullshit like quasigroups. At any rate it just means the numerator is multiplied by the multiplicative inverse of the denominator.

Why don't you graduate kindergarten before you reply.

>> No.9732375

>>9731753
I agree wholeheartedly with this. OP needs to think about what he has said with the class and whether or not kids could have actually answered the question correctly with the information he gave them. If he hasn't he should apologize to the class and not grade the question, it would be a good lesson in humility for his students.

Personally my background in commutative algebra would have me extend the definition of fractions to "an expression of the form [math]\frac{p}{q}[/math] where [math]p,q[/math] are elements of a commutative ring and [math]q[/math] is not a zero divisor," but your definition is accurate enough since middle school kids are usually not tinkering with coherent sheaves yet. OP seems confused about the concept of zero divisors and probably needs remediation in abstract algebra.

>> No.9732392

>>9732331
That's objectively wrong you dipshit.

>> No.9732403

>>9732392
>induring this plebian thinks a rational is a fraction and not an equivalence class of sets with certain properties on it.
How embarassing for you.

>> No.9732405
File: 23 KB, 274x205, irrational2.png [View same] [iqdb] [saucenao] [google]
9732405

>>9728697
Then we are doomed.

>> No.9732423

>>9732331
is [math] a\cdot b^{-1}\,;\ b\neq0 [/math] a fraction?

>> No.9732437

>>9732405
>durr they used a term loosely on my first year abstract algebra for dummies course, therefore the definition of fraction now entails all that bullshit XD
Also your pic equals infinity because of how my measure theory course defined x/0 for non zero x.

>> No.9732494

>>9732423
Fraction is the notation
[math]\frac{a}{b}:= a\cdot b^{-1}[/math] where [math]b\neq 0[/math]

>> No.9732503

>>9732494
oh, and [math]0[/math] is the addiive identity, if you have one.

>> No.9732686

>>9732072
This post was kind of dumb but you also have a point in that there's a difference between a fraction and a fractional number.

>> No.9732698
File: 59 KB, 540x595, 20110408.gif [View same] [iqdb] [saucenao] [google]
9732698

>>9729491
>>9729566
>>9729582
https://www.smbc-comics.com/?id=2208

>> No.9732700
File: 3 KB, 286x176, CDA09A8BD0804CBF910FAC7E0EB911A1.png [View same] [iqdb] [saucenao] [google]
9732700

>>9728694
Root 2 over 1

>> No.9732731

>>9728927
The quesiton is not ambiguos because 1/0 is not a fraction, its not even well defined. I suppose the point of the question was to shoe if you ubderstand the proper definition of an irrational number, which id that it can be expresded as a fraction of two integers. Sqrt(5)/2 is a valid answer.

>> No.9732772
File: 45 KB, 540x595, 1525998066278.png [View same] [iqdb] [saucenao] [google]
9732772

>>9732698
why the hell was the original encoded as a damn gif

>> No.9732983

>>9728694
infinity is not a number.

>> No.9733003

>>9732983
It is in [math] \mathbb{R}^* [/math]

>> No.9733005

>>9728694
If we were to organize orders of infinity as a number system and divide infinity with an order of 1 by an infinity with an order of zero (in other words, a finite number), the result is infinity. That's outside of rational number's space.
Kid gets marks imo.

>> No.9733180

>>9728694
>https://en.wikipedia.org/wiki/Division_by_zero
brainlets itt
OP asked for a fraction that is not a rational number
the answer exists in the space of all fractions not rational.
1/0 is still a fraction, although its undefined, it exists in the space of all fractions that are not rational.

>> No.9733195

>>9728694
I’m the kid who wrote that and fuck you mr Stanley you smell like a honey ham. Indeterminate type is fraction give points poop head

>> No.9733207

>>9728694
>1/0
...is indeed a fraction (even though indeterminate)
and certainly not a rational number, because indeterminate.
10/10 for seeing farther than the uncon/sci/ous spergers
who can't distinguish between fraction and rational number.

>> No.9733229

Too bad this argument is pointless a "fraction" is undefined. But the only way the kid could be wrong is if you define fraction as not having a zero in the denominator. But the are sets of non negative numbers where 1/0 = infinity. So defining fraction in that way would conflict with this notion. So I'll say the kid is right

>> No.9733234

>>9732437
>first year abstract algebra for dummies course
/sci/ implying that abstract algebra is no longer rigorous.

>> No.9733235

>>9732494
see
>>9733229

>> No.9733242

>>9732698
>>9732772
FTFY

>> No.9733248
File: 126 KB, 540x595, math-student-mathematician.png [View same] [iqdb] [saucenao] [google]
9733248

>>9733242
forgot the damn image

>> No.9733665

>>9733248
>It can't be expressed as a relationship between two numbers

[math]\pi = \frac{\tau}{2}[/math]

>> No.9733675

>>9733665
Pretty sure xe meant "whole numbers" smartypants ;)

>> No.9733713

>>9733675
>xe
lold

>> No.9733730

>>9733665
[math]\pi = \pi / 1[/math]

>> No.9733790

>>9728694
[math]\text{NO! by definition, fractions are the equivalence classes of the form }[/math]
[math]\frac{a}{s} := \{(b,t)\in R\times S : (a,s)\sim (b,t)\}[/math]
[math]\text{Where }R \text{ is an integral domain and }S = R\setminus\{0\}[/math]
[math]\text{With the equivalence relation }\sim \text{given by:}[/math]
[math](a,s) \sim (b,t) \iff at = bs[/math]

[math]\color{red}{\text{CLEARLY }\frac{1}{0}\text{ IS NOT A FRACTION BECAUSE } 0\not \in S}[/math]

>> No.9733880

You give him the points but you explain to the class why that's not a valid answer, since apparently you didn't teach it properly.

>> No.9734116

>>9728694
depends on what you mean by "fraction"

Is just using the symbolic "a/b" form enough? Or does it need to be resolvable to a real number via division? It's not a number except in sets that include the point at infinity.

>> No.9734914

>>9728694
give the lad a right answer, undefined sure as hell isn't rational

>> No.9734946

>>9728694
You probably taught him that rational numbers should be ratios between integers, with zero on the denominator being the exception, he remembered this fact mid-test and thought that this was exactly what you wanted him to do.
How you should approach his answer depends on how deep of an understanding of math you want your students to have. That's all

>> No.9734960

>>9733790
Why do freshmen love to write so much to say so little

>> No.9735047

>>9733790
You could just say you excluded zero from your definition. But why not exclude some other number, like 4?

>> No.9735173

>>9728694

Yes

You got pwned

>> No.9737042

>>9728694
> it is a fraction
> it is not a rational number

sure

>> No.9737079

A rational number is just a quotient of integers. 0 is an integer. 1 is an integer.

therefore 1/0 is a rational number.

>> No.9737096

>>9728694
you asked for a fraction and not for a fraction that makes sense. give that kid some props

>> No.9737124

>>9737096
1/0 is not a fraction by definition. It's not a "fraction that doesn't make sense"

>> No.9737148

>>9728694
Regardless, you shouldn't be teaching anything if you had to ask this question.

>> No.9737159

>>9728694
Your student outwitted you. Humble yourself.

>> No.9737266

>>9728706
pi alone is a fraction retard

>> No.9737277

1/0 is not even a fraction, braindead

>> No.9737320

>>9733195
Kek

>> No.9737352

>>9728748
>I will still mark it wrong
At least give him half credit. He followed your instructions, prick.

>> No.9737433

>>9737124
>1/0 is not a fraction by definition
State the nondefinition, then.

>> No.9737454

How can you have 1 over nothing? How is one of something part of nothing?

>> No.9737464

>>9737454
Conceptually there's no real meaning to it, but he literally wrote out the format of a fraction and made it irrational. When you get to calculus you learn why you can't do that; but this kid followed OP's instructions exactly - just with little regard to context. I believe that's what they call a "mathematician's answer".

Also I'm assuming OP had never mentioned indeterminate forms. If he did, it's all on the student; if he didn't, the kid deserves half credit at least.

>> No.9737472

>>9728694
Technically he is right. 1 over 0 is a fraction and is neither rational nor a number. It's something else.

>> No.9737477

I feel like OP just wanted to ask if [math] \frac{1}{0} [/math] is a fraction and made this larp to trick us into indignantly answering him.

>> No.9737645

>>9733675
>xe
stfu

>> No.9737710

>>9728694
Yes, of course.
A fraction is a symbolic construction, so
1/0, apple/6, and $/北京 are all fractions.

But none is in the set R.

>> No.9737711 [DELETED] 

>>9728694
That's a shitty and confusing question.

>> No.9737716

don't mark him wrong. If you punish him for it then He will lose his playfulness with math concepts

>> No.9737787

>>9737266
BOOM HEADSHOT

>> No.9737891

You should punish him for his out of the box thinking. We cant have this shit in our education system. The only correct answer is pi/2 because that is the answer you wanted out of him.

>> No.9738039

>>9733234
You have to admit that abstract algebra is pretty fucking easy though. They should really start teaching it in high schools.

>> No.9738057
File: 1.65 MB, 360x359, fsd.gif [View same] [iqdb] [saucenao] [google]
9738057

>>9737891
This is some fucking top-tier sarcasmkino.

>> No.9738217

Just fot the fact that this discussion is happening I think you should give him at least half a mark.

>> No.9738222

He's right. You shouldn't ask such vague questions on a test

>> No.9738367

>>9728694
He's right

>> No.9738374

>>9728694
1/0 is a value expressed as a fraction and it is very irrational
Therefore, the kid is right

>> No.9738377

>>9738374
well not irrational, but definitely not rational

>> No.9738511

>>9738377
if it's not rational, it's irrational. and if it's not irrational, it's rational. you can't be neither and then be like quasi-rational or something. kid's right.

>> No.9738523

>>9731753
the kid's wrong, but the fact that you're not sure about it makes me suspect that the definition you taught was unclear or ambiguous, and that he might have been interpreting *your* definition in a reasonable way.

>> No.9738524

>>9738523
oops replied to wrong post, meant to reply to OP

>> No.9738603

Write a prime divided by it's square root e.g:- 2/sqrt(2)

>> No.9740541

>>9733675
>Pretty sure
You aren't sure how to spell "he" fgt pls

>> No.9740544

>>9737454
>nothing
Zero is not nothing. It is a number, it is the additive identity,
it is a place-holder in our numeration, it is the cardinality
of the Empty Set; it is therefore something, whereas nothing is nothing.

>> No.9740741

>>9728694
Why teachers write simple mathematic requests as:

Less than the quoficient of 5 and a number x as the dividend of y more than seven

???

I dont even want to know how this would sound in common core language for kids today

>> No.9741058

>>9731709
really? you need a proof to see that √2/1 is not rational?

>> No.9741416

>>9728694

1/0 is a fraction, tho it's not a real number; but you didn't specify that the fraction be a real number did you? 1/0 is not a rational number. so even though it's a loophole answer, he is right. Don't you feel stupid, a middle school kid just schooled your ass. next time just say that the denominator must be non zero.

>> No.9741419

>>9728888

it's valid under the extended real line.

>> No.9741425

>>9728706

pi/2 is not a fraction. the definition of a fraction is a/b where a and b are integers. usually b is defined to not be zero tho in some number systems that is ok.

>> No.9741428

>>9737266

no it's not. pi is an irrational number meaning it can not be written as a fraction. the closest fraction to pi is 22/7.

>> No.9741466
File: 962 KB, 171x172, alex_jones_suspicious.gif [View same] [iqdb] [saucenao] [google]
9741466

>>9741428
Pi/1
Brainlet

>> No.9741504

>>9741428
>the closest fraction to pi is 22/7
think about what you just said for a minute

>> No.9741553

>>9741504
behold /sci/ intelligence

christ there needs to be a culling of sub 130 IQs on here
/pol/ is legitimately smarter than you retards

>> No.9741975

>>9729482
You're retarded, that's not what the question was. It was something not a rational number i.e. outside the set of rational numbers. It's up to interpretation whether real numbers were implied or not.

>> No.9741987
File: 1.00 MB, 2000x2000, 4chan_iq.png [View same] [iqdb] [saucenao] [google]
9741987

>>9737266
>>9741428
>>9741504
>pic related

>> No.9742176

>>9741987
>Lit defeats sci
>K scored higher than expected


anyway, IQ per board never averages the 120+ mark ever, meme graph is meme graph
not that we tested individuals in any propper way

>> No.9742185

>>9741428
And 22/7 is an irrational number, what do you know.

>> No.9742188

>>9742176
t. insecure /pol/ crossposter

>> No.9742205

>>9742188
I am a sci poster, so please make that: t. insecure sci poster

>> No.9742952

>>9728694
Unless you defined a fraction in a super specific very explicit way I would just I've him full marks. It's an original, creative answer. If you wanted a better answer you should have made the question clearer. The fact that you're not even sure whether he's right or not just means you should give him full marks.

>> No.9743738

>>9728694
Well, 1/0 is technically not a ration number. Furthermore, as it is division by zero - it was a very irrational thing to write, which is not rational. Give points.

>> No.9743751

>>9728694
Kid is right. He wrote a fraction that is not a rational number.