What is both finite and infinite? The length of AB is finite, and is never infinite. The number of points that can be described along AB is not finite, and is never finite, hence the existence of the bijuntion between that segment and any other. Neither is both finite and infinite.It has to do with relativism because something can't be both finite and infinite at the same time with respect to the spatial, yet it is so. — Gregory
I can think of at least 3 things very wrong with this statement. For one, what's the difference between X being half Y and X being eternally half Y? I mean, 5 is half of 10, and no matter how long I wait, 5 will remain half of 10, so I suppose it is eternally half of 10, but saying it that way doesn't make '5 is half 10' more true.The odd numbers are eternally half the natural numbers, so there is no way at infinity they can be equal. — Gregory
What, exactly, is finite and infinite? Subdividing a finite segment doesn't affect its total length, so its finite length is unchanged. Also, what's the difference between 'endlessly' and 'endlessly, to eternity'? That's twice you've used that redundant modifier like it means something different than its absence.If you can subdivide a segment endlessly, to eternity, it's finite and infinite.
It's a bridge though to Eliatic realms however, a secret door though that mathematicians don't know about — Gregory
What, exactly, is finite and infinite? Subdividing a finite segment doesn't affect its total length, so its finite length is unchanged. Also, what's the difference between 'endlessly' and 'endlessly, to eternity'? That's twice you've used that redundant modifier like it means something different than its absence. — noAxioms
For one, 'infinite' is not an amount, and 'literal infinite' is no different than 'infinite'.Do you deny that it is unintuitive to be able to divide something finite a literal infinite amount of times? — Gregory
You have weird intuition. — noAxioms
I might not. You're the one making the suggestion and then driving your own assertions to obvious nonsense conclusions.If I take a cube, and divide it in half, and then again, ect to infinity and then line them all up biggest to smallest, what is the smallest? ...
You might say "there is a limit". — Gregory
Exactly so. So maybe try it without positing a last term in the infinite series.So we have a huge paradox here.
Physical now? A physical cube-shaped object has a finite number of particles in it and can only be divided so many times. There is a smallest part at the end of the sorted line and it has a color if you're going to abstractly assign colors to the even and odd ones.Does the series go off into the physical horizon forever?
For you, at least? What does that mean? If that means you have run for yourself a nice warm tubful of ignorance and are now taking a public bath in it, please spare us the exhibition(ism).For me at least, this example causes two intuitions to collide, which is the essence of relativism (that is, that truth has no essence).
True? — Gregory
Eh? This merely says you don't know your subject - at all!I am tired of reading that crazy man "Cantor proved" so and so. We know nothing of infinity. The odd numbers are eternally half the natural numbers, so there is no way at infinity they can be equal. To say otherwise is to make infinity a number. That is as air tight an argument as anything Cantor wrote. — Gregory
A physical cube-shaped object has a finite number of particles in it and can only be divided so many times. — noAxioms
The truth has no essence? What does that mean? — tim wood
So what's your point? — tim wood
Finite figures have no actual points, but infinitely many potential points. Dimensionless points are not parts of the figures, they are something that we artificially impose on them for particular purposes, such as marking and measuring. Every part of a one-dimensional line is a one-dimensional line, every part of a two-dimensional surface is a two-dimensional surface, and every part of a three-dimensional solid is a three-dimensional solid. Figures of lesser dimensionality--a point on a line, a point or a line on a surface, and a point or a line or a surface on a solid--are limits that we create by arbitrarily dividing the whole into parts.If finite figures have an infinity of points, that is paradoxical. — Gregory
That's what relativism means. Truth is not truth — Gregory
1) how can something have no spatial final term but be finite
2) why can't you compare two infinities by first combining the cardinality with the density in each? Isn't this how you truly compare infinities? — Gregory
Comparing infinities using different measures (density vs cardinality) that contradict each other proves the mathematicians don't have any idea of what infinity is — Gregory
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