From a pure logic perspective, there is no concept of a monad. There is no need for such a concept and no phenomena are explained by it. Yet all metrics are defined by constraints within the bounds of an endless field. For example, one inch is an arbitrary gauge inside of an infinitely large "space". We are saying "this big of fractional piece of the universe in one dimension, is one inch". Ultimately, all distances converge to zero as a fraction of the whole, as it is simply division by infinity.
It would thus make sense that the infinite set is the "monad" of numbers, the unitary from which each number is derived as an infinitesimal fractional portion. Of course set theorists have thought of similar ideas before however it is possible that adopting such a top down approach could resolve issues like Russell's paradox.
Originally posted by mmQ
Like there's an infinite amount of numbers between 1 and 2 yet 3, 4, 5 etc. all still exist.
Yes indeed. A good way to think about it is to think of a circle; why is there only so much rotation for a circle to cover? Why aren't there 9000 of the currently defined degrees, rather than 360? The answer is that the currently defined single degree is just a set or range of angles that contains an infinite amount of elements therein. We simply divided that particular infinite into 360 different degrees by using limits (the calculus concept). This is why radians are useful, because it is a unit derived from the internal mathematical logic of what a circle even is, but there's still no real explanation for why that ratio is 4pi radians to a full rotation and not 6pi radians. Nobody really knows. But it doesn't matter because we just take that whole and subdivide it. Even if we had more space, we could just have 6pi radians or 420 total degrees, it's just more places for those same sized units to go.
You're saying units of measure have no meaning in that the scale of infinity immediately renders them useless?
Infinity is one of the hardest concepts for my brain to accept.
Like on pen and paper it's easy to understand, of course, but whenever I start picturing infinity in my head it scares me a little. Especially infinite time.
Originally posted by DietPiano
You're saying units of measure have no meaning in that the scale of infinity immediately renders them useless?
Infinity is one of the hardest concepts for my brain to accept.
Like on pen and paper it's easy to understand, of course, but whenever I start picturing infinity in my head it scares me a little. Especially infinite time.
No, it doesn't render them useless. It's just defined as some arbitrary subdivision of space or whatever other thing.
But don't let infinity scare you. Let me put it this way: wouldn't it be weirder if things just ended? Like if 1000 was just the biggest number and there was no concept of anything beyond a thousand of a thing?
cupocheer
Space Nigga
[unwillingly condescend the dp]
Originally posted by Captain
No, it doesn't render them useless. It's just defined as some arbitrary subdivision of space or whatever other thing.
But don't let infinity scare you. Let me put it this way: wouldn't it be weirder if things just ended? Like if 1000 was just the biggest number and there was no concept of anything beyond a thousand of a thing?
But, aren't you incorrect, Captain?
If we should agree that the number 1,000 is finite then isn't 1,000, also, infinity?
Keeping in line with the theme of this thread, a bound implies an opposite side to that bound, because the point of a constraint is to restrict something inside a larger space. That is by definition an unapproachable mystery. No bound implies no other side; you are already experiencing the infinite field of numbers that stretch backwards and forwards to negative and positive infinities, and outwards to complex infinities. There is no mystery, just magnitudes we are familiar with. We have all the room we need to stretch our legs.
cupocheer
Space Nigga
[unwillingly condescend the dp]
Ah, your theorum whetted my meager mental capacities, so, one savant to another, I shall pull my legs up under the throw and incubate. 'Tippa the cap, Cap.
[When utilizing a logical numerical as a finite all resultant equations can only be infinite.] (Don't shoot the messrnger.)
cupocheer
Space Nigga
[unwillingly condescend the dp]
Bebe! I saw you from a distance a whilr back but you passed out of my view closely trailing an attractive young blonde. muah! no loco in de coco bambino:'
Ensign Galm
African Astronaut
[specifically erupt this tetrachloromethane]
Originally posted by Captain
I still don't understand how someone that's so seemingly chill can simultaneously be so asspained when people discuss things they find interesting.
