This is why infinity as a concept is retarded

Hi Wildberger

The area of the plane x=0 is infinite. So is the area of the plane x=1. These are two separate planes that don't intersect, but both have infinite areas.

>If you define something as an "area", then there must also be something that isn't an "area", otherwise you cannot define it as such, which means it isn't infinite.

what the fuck kind of broken ass logic?

Bullshit.

What's separating these areas if they are infinite? It doesn't work, infinity does not have a beginning and an end so they can be separated.

This shit is the reason why I went into engineering instead of maths

>What's separating these areas if they are infinite? It doesn't work, infinity does not have a beginning and an end
They're separated by an infinite volume defined as 0

For an area to be an area it must be finite, otherwise there's no starting or end point to do anything with that area.

what if you have the lines y=x and y=x+1,
they both have infinite length and they're separated by the little strip of the plane in between them

>For an area to be an area it must be finite, otherwise there's no starting or end point to do anything with that area.

useless, you just pulled that straight out of your ass

>For an area to be an area it must be finite
It's just wrong

>otherwise there's no starting or end point to do anything with that area.
What the fuck do you mean "do something"? We're talking about mathematical ideas here.

You're either trolling or you have some reading to do.

>this is an area
>except there are no boundaries
where's the fucking area then???

>Riddle me this: There are infinitely many natural numbers, but not every number is natural.

Numbers aren't actually separate either. A number is the number it is, as well as every number it is not.

Length is again a finite concept - they cannot be infinitely long because length requires a beginning and an end.

Prove it wrong.

Do calculations with.

You don't know what you're talking about.

what is the area of a circle with a variable radius. now then, what is the area of a circle whose radius is infinite.

Koch Snowflake curve
Infinite length line enclosing a finite area
No calculus needed. Get used to it

>Prove it wrong.
DUDE you just made it up im not fucking proving your own false garbage.

>Length is again a finite concept - they cannot be infinitely long because length requires a beginning and an end.
the beginning is [math]x=-\infty[/math] the end is [math]x=\infty[/math]

>Do calculations with.
you can do calculations with infinite areas

>variable radius

That's finite.

> radius is infinite

Impossible. There'd be no circle (which is a finite sized shape).

>−∞
>x=∞

You cannot represent infinity using symbols which themselves are finite. Infinity does not have a beginning and end.

>Impossible
No such thing as impossible in Math brainlet, its called abstraction

its called abstraction. How you write something down as ZERO impact on the properties of the actual thing the symbol represents you brain dead imbecile.

>you cant write 2 with one symbol, it represents an amount of two things
Kys

Post just before yours proves you're wrong.
Infinite length boundary line.
Not my fault if your screen only supports finite resolution.

Oops, sorry You were agreeing lines CAN be infinitely long.
Misread you.

its cool, i misclick all the time

Abstraction cannot represent infinity.

It does when you're trying to give infinity a beginning and an end.

>Abstraction cannot represent infinity.

Why not

Where's the line?

the border of the black and the white

Because infinity does not have a beginning and end.

That's a shape, not a line.

>Because infinity does not have a beginning and end.
Not justification

1 doesn't have a beginning and end, its a goddamn fucking number

This is why OP as a faggot is retarded

Not at all, your intuition is just shit. Teenagers can intuit the plausibility of the notion, and correctly understand same, to themselves.

Among conventional (Euclidian) geometric figures, the figure having a finite surface area and a finite volume is trivial, and the figure having an infinite surface area and a finite volume is also straightforward to intuit (if a bit strange at first), provided that the surface area is /shaped/ appropriately (/shape/ and /infinity/ are independent qualities of a thing). It is even straightforward to intuit a figure with both infinite surface area and volume: imagine a set composed of infinitely many disjoint spheres, cubes, etc, , forming a lattice. All this, because what is /infinite/ may /bound/ what is finite/, or even another /infinity/. And it is in the nature of geometric objects that the exterior should bound the interior, where both exist. But the converse of the former is the only true absurdity.

The only notion which is an absurdity among the four possibilities, is that a figure with an infinite /volume/ may be bounded by a finite surface area. And likewise in the analogous two-dimensional cases where the appropriate words are replaced by "perimeter", "area", etc.

>1 doesn't have a beginning and end

Exactly my point.

That IS a line. The boundary between black and white. Maybe I should have picked an illustration which had white on both sides of the line, but that doesn't alter anything.

>The only notion which is an absurdity among the four possibilities, is that a figure with an infinite /volume/ may be bounded by a finite surface area. And likewise in the analogous two-dimensional cases where the appropriate words are replaced by "perimeter", "area", etc.

In Euclidean geometry, yes/
In hyperbolic geometry, perfectly legit to have an infinite area (and infinitely long lines) bounded by a finite perimeter.
In fact, most of Relativity uses hyperbolic geometry. The event horizons of black holes have a circumference but (possibly) infinite radius. In the reduced dimension analogies you see drawn, the center of the "funnel" is stretched infinitely far out of the flat space "plane" which surrounds the hole.
All a matter of picking the appropriate metric for the situation.

It's a finite shape in a finite area. You cannot apply length to something that doesn't begin or end.

BOI the definition of area and volume doesnt involve length. The area can be infinite, if you know anything about linear algebra it would be obvious to you. Fucking brainlet ass /b/tard coming over here stirring shit kys cunt

If it was you that posted the Koch snowflake you said it was an infinite length line enclosing a finite area.

>t. brainlet

>BOI the definition of area and volume doesnt involve length
Prove the area of a square without using length.

Na different guy. I literally study this as a part of my course. The concept of area and volume as parts of mathematics as a whole only makes sense if you allow for infinity to exist in both cases. (basically since they are defined by planes, in turn defined by infinite vectors). Another way to think about it is that in real life, we have no reason to believe that infinitisemally small volumes exist (and then by symmetry, infinitely large volumes)
TL;DR basically the whole argument boils down to not being a fucking brainlet

What about C, where there s no order property and no -inf

Peasant.

>LMAO GOT EM MOM HERE COME LOOK I MANAGED TO STRETCH MY CHEETO CRUSTED FINGERS TO TYPE SOME RETARDED SHIT ON A MONGOLIAN BASKET WEAVING FORUM

Calculus is not about adding infinities together but about working your way towards infinity through limits. Mathematics can't work with infinities as a standalone concept (see 1/0 or 0/0)

There exist a linear isomorphism w/ determinate 1 from C to R2 so volumes in C correspond to volumes in R2

Fascinating, so a black hole just looks like a 4d funnel

>I literally study this as a part of my course

Of course you do, doesn't mean they're right. Professors are just spewing what they've been "taught".

Infinity is a concept that is grossly misunderstood in mathematics. Trying to apply it to finite concepts is completely illogical. All numbers are a representation of infinity themselves, we just put different labels on them 1, 2, 3 etc.

You cannot work towards infinity because there's no starting or end point.

>BOI the definition of area and volume doesnt involve length
Measure Theory kid, educate yourself on some Lebesgue measure. Area and volume are exactly the surface of the square or the length or the line

Oh! I tie a string in a loop and it doesn't have a length?

Look up Koch snowflake. Each additional lever of detail added multiplies the length of the boundary line by 4/3rds and the procedure never ends.
Yet the area is clearly finite since I can draw a circle around it.

Of course the Horn is only an abstraction which can't be constructed in Real Life because matter can't be subdivided into an infinite number of "mathematical points".
Same reason the Banach–Tarski Paradox can't be executed in practice.

>unironically uses Measure Theory
>tries to sound intelligent
Pick one boyo

Define an order relation on R2

>Oh! I tie a string in a loop and it doesn't have a length?

Was the string infinitely long in the first place?

>multiplies the length of the boundary line by 4/3rds

So there is finite length then?

>upset undergrad that doesn t understand the nuances of MT
>fucking retard that doesn t know what he s talking about
Choose one

>unironically thinks that measure theory is in any way brainlet

kys, maybe learn it before you shit on it

Yes you can, infinity is bigger than the norm of any number, therefore you can start counting towards it from any finite number.

It isn t a curve (line), it is a family of lines whose length tends towards infinity. The snoflake in the image has finite length

Infinity is not a number, it is a property of all numbers.

>it is a property of all numbers.
no

infinity is the size of the set of the integers you fucking retard

>infinity is a property of a finite number
Out

>infinity is a proprety

>infinity is the size of the set

You're applying the finite concept of size to infinity.

∞00000000000000001.0000000000000000000∞

A number is represents itself, and every number it is not. They are infinite.

No, it was a finite length before I began. And it still has a finite length after I complete the knot and snip off the loose ends.

The snowflake is DEFINED as having been generated by an infinite procedure. As I said, not my fault your limited monitor can't display it in full detail. You have to zoom in, just like you would the Mandelbrot Set.
And it IS considered a curve despite having no tangent defined at any point. It was called "pathological" when introduced but is now accepted as a curve, as precisely defined as a circle is.

>No, it was a finite length before I began. And it still has a finite length after I complete the knot and snip off the loose ends.

So how can infinite length exist?

>You're applying the finite concept of size to infinity.

And you're saying that none of the properties of the real numbers apply to infinity, which is far more unreasonable.

Not following.

>brainlet rejects concept his mind is not strong enough to comprehend

this is stupid and should be deleted along with all similar threads

Pythagoreans figured out millenniums ago that when faced between trusting logic or intuition, you should pick logic. What you are calling logic is intuition, you think you know what it is but you don't.

What's illogical about it?

>Area and volume are finite concepts
this

>Infinite Area and finite Volume
Is perfectly logically valid. Now on the other hand,
>finite surface area but an infinite volume
Would be wrong.

Saying that area and volume are finite concepts is illogical because it has no grounds on math. It is something intuitively true, just like "the square root of 2 is a rational number" used to be an intuitively true concept. Both are logically wrong.

You don't need an order relation to define volumes.

given a line A from 0 to n and a line B from 0 to n+1 the length of B is larger than the length of A. so the length of a line from 0 to [math]\infty[/math] is larger than every other length, which is just the definition of infinity. So its logical to say that the length of a line that doesn't end is equal to infinity.

An area = size
Size = finite
Infinity = no beginning and no end

A size must have a beginning and an end to be a size. Therefore a size/area cannot be infinite.

Really lazy attempt. Consider yourself lucky Veeky Forums falls for baits this easily.

This begins with the false assumption that a line can go to infinity. You're applying a beginning and an end to something that doesn't have one.

I'm not the OP, nor am I baiting.

>A size must have a beginning and an end to be a size.

That's where you're wrong, kiddo.

en.m.wikipedia.org/wiki/Measure_(mathematics)

OP, the object in you're picture cannot exist in this universe as far as we know
zeno's arrow and/or geometric series is a far more reasonable introduction to infinity as a concept outside of counting

That's making the same mistake, the diagram has a finite line with a beginning and an end.

you're far too deep into your own ass that you can't stop using your intuition, and even worse thinking that your intuition is logical
you're everything wrong with this world

“When the wise man points at the Moon, the idiot looks at the finger.”

...

Since you seem to have some kind of reading deficiency, allow me to refer you to the following sentence:

"Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X."

It's literally a part of the definition.

I didn't come to my conclusion because I felt like it, it's based on conscious reasoning. If it's so illogical then you need to prove why.

Can you point to infinity?

Don't punch me punch the "intellectuals" who came up with this deliberately confusing shit.

Meaningless jargon. You cannot apply infinity to finiteness, it's as simple as that.

>argues with a definition

>Can you point to infinity?

Meaningless definition.

Didn't think so.

>Meaningless definition.
>Standard definition used by mathematicians is 'meaningless' because I'm retarded and incapable of comprehending it.

Seriously, do the world a favor and kill yourself mate.

Also, shouldn't the diagram look more like this?

Measures are non-negative.

They're just as lost as everyone else.

So zero is the beginning? Not infinite then.