This guy walks up to you in the middle of the night in an alley and says, "Hey kid, wanna see that there are different kinds of infinities?"
What do?
cry
>>8046544
whip it out and say:
>I'll show you mine if you show me yours?
>>8046544
Prepare my boipussy to get destroyed.
>>8046544
I turn 360 degrees and walk away.
>>8046544
I show him the method of forcing.
>>8046544
I tell him infinity isn't real
>>8046544
>implying there is even one infinity
you can't geometrically construct infinity even once
nobody has ever done it
infinity exists on a level of abstraction that would give Plato pause; infinity might not even exist in his ethereal "world" where all the numbers exist
>>8046752
But mathematicians would never waste time on such pointless stupid bullshit!
>>8046752
>you can't geometrically construct infinity even once
Draw 2 unequal points A and B and a line through them. The number of points on that line is infinite.
Proof left as an exercise.
(Hint: consider a point C not colinear to A and B. Prove that for any finite set of lines S between C and a point on AB there exists a line L not in S)
>>8046785
>consider a point C not colinear to A and B
does such a point even exist in the general case?
I'm not convinced.
>>8046785
> A and B and a line through them. The number of points on that line is infinite.
because you haven't defined point accurately enough. if you do define a point accurately enough, there will be a finite number of points. the only limitation is your accuracy in measuring
>>8046785
What is a point?
Your definition of point is still abstract notion.
>>8046778
the only correct answer
>>8046544
Why can't you use the diagonal argument with integers?
>>8047018
Because the diagonal arguement always results in a number with infinite digits.
Integers are neccesarily finite.
>>8046785
here are two unequal points
they are very very close together
so close, in fact, that any attempt to measure the distance between them will be fraught with extreme difficulty
and they're connected by a line which I define to be the size of a single point
so fuck you, i constructed a line with one point on it
Continuum hypothesis + Cantor BTFO
pic related
>>8047092
>and they're connected by a line which I define to be the size of a single point
A point which has any form of "distance" is a circle.
>>8047092
But you still dont know what infinity is.
>>8047106
i don't think you understand
there are two affine points connected by a line which is only as broad as one affine point
I don't see any circles here
I would begin to preach on constructive mathematics and the notion of potential infinity as opposed to actual infinity
hopefully this would allow FoM to entirely skip over that embarassing religious platonic phase
>>8047115
>The plane doesn't have Archimedean property because I say so waaaah
