arbegla gnikcuf

[Fucking Algebra No.5701708]

Fucking Algebra.

In my personal fucking professional opinion
<div class="math">S=\mathbb{N},x\circ y := \min (x,y)</div>, is at least a fucking monoid. Why you ask? because the neutral element is <div class="math">n = \infty \in \mathbb{N}</div>

>butbutbut, professor exclaims, OP, thou art a fagget! for infinity is not a natural number!

why of course it is, whatever infinity may be, it will certainly be a natural number, because I defined it as such!

>no it's not, for "infinity" is not a number

perhaps it isn't - and even if that is true, what disqualifies it from being the neutral element? It is in the domain of naturals, and you can compute just fine with it.

>it's not a fucking number. also, you can't have an inverse element.

who the fuck cares? it's at least a monoid. is it your definition that excludes the infiniteth natural number and the concept of infinity from set theory? is that an axiom?

>I guess you're right it does come down to definition. In some instances, for example, people include 0 in Reals, and in others they don't.

...

smallvictoryplz.

still not satisfied.

<div class="math"> S=(\mathbb{R},\cdot )</div> is an abelian group.

>OP, are you being a faggot again, what is n/0

n=1 and the conjunction <div class="math">0 \cdot 0^{-n}</div> can be expanded into <div class="math">0*\left ( \frac{1}{\lim_{1\rightarrow 0}} \wedge \frac{1}{\lim_{-1\rightarrow 0}}\right )</div>

<div class="math">\frac{1}{\lim_{1\rightarrow 0}} \wedge \frac{1}{\lim_{-1\rightarrow 0}}</div> itself would yield an empty set, however, distributed it would be <div class="math">\left ( \frac{0*1}{\lim_{1\rightarrow 0}} \wedge \frac{0*1}{\lim_{-1\rightarrow 0}}\right )</div> without losing generality the zeroes cancel and and a junction of 1 and 1 equals 1, and since n=1, an inverse element exists for 0. it is also commutative.

>OP, that's not how math works

prof, you're an excellent teacher!

..

...

thumbs up and reblog if I gave you cancer.

also yes, I mad.

[Anonymous No.5701723]

Thank you. I now know what it's like to have a mental illness.

[Fucking Algebra No.5701749]

>>5701723

please, what's my mental illness, I need to know. fix me anon, fix me!

[Anonymous No.5701821]

um i don't think so
let's suppose what you're saying is true and <span class="math">S=(\mathbb{R},\cdot )[/spoiler] is an abelian group
0 has some inverse element let's call it i dunno <span class="math">\alpha[/spoiler] so that <span class="math">0\cdot \alpha = 1[/spoiler]
an abelian group had better be fucking associative, so
<span class="math">2\cdot(0 \cdot \alpha) = (2 \cdot 0) \cdot \alpha[/spoiler]
<span class="math">2\cdot(1) = (0) \cdot \alpha[/spoiler]
<span class="math">2 = 1[/spoiler]
oops look like you need to reevaluate your little theory ya got there``

[Anonymous No.5701834]

In my personal professional opinion this is blue. I stopped caring about colors when I was told otherwise.

[Anonymous No.5701856]

thanks for giving me cancer

[Anonymous No.5701861]

>even in your own argument you sound like a whiny dick

[Anonymous No.5702217]

>>5701861
I thought that was hilarious anon, 8/10

[Anonymous No.5702245]

>why of course it is, whatever infinity may be, it will certainly be a natural number, because I defined it as such!

Then you're defining the natural numbers to be something different to the rest of us.
I can prove the Riemann Hypothesis that way.

[Anonymous No.5702249]

>there are people out there that need to deal with OP every fucking day.

[Anonymous No.5702309]

Well considering that math is _supposed_ to be an approximation of reality, it doesn't really seem logical to explain a value as increasing without it being a function of time/whatever. I guess that's why everyone look at it as an infinite set of values.