If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and… then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities, and… (infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and…) continues forever. and that continues forever. and that continues forever. and that continues forever. and that continues forever. and…..(…)…
>>16854823They may or may not coalesce, thoughbeit, depending on whether or not there's a one-to-one mapping between them.
>>16854823Mathematicians spend way too much time worrying about this gay shit. It would be like a Carpenter having a mental breakdown thinking of the infinite number of things he could build out of wood. No one gives a shit brah
>>16854833But it’s based
>>16854823It gets worse. There are infinitely many irrationals between any two rationals AND infinitely many rationals between any two irrationals. To make matters worse, there are an equal number of numbers between 0 and 1 as there are between -∞ and +∞. As a matter of fact, this set (-∞,∞) is isomorphic to any set of real numbers (x,y) with x < y, even 0.999999... and 1, where here I use the ... notation to imply Graham's number of nines (not infinite, finite). Mathematicians will unironically look you in the face and tell you there is nothing wrong with this.
>>16854823Why the fuck do you keep posting this thread? You posted this exact same thread on /x/. Am I replying to a fucking AI or what?Like I fucking told you already, look up surreal numbers dumbass. Or better yet, just look up dedekind cuts. Nothing you are expressing is a deep epiphany or insight into anything. You sound like a retarded stoner.
>>16856082>Mathematicians will unironically look you in the face and tell you there is nothing wrong with this.See exhibit A>>16856086
>>16856090Because you're not expressing anything important. Just fuck off already. People like you are so goddamn obnoxious. Go get a job at 7-Eleven and never post here again. You will never understand math and you will never be a scientist or even an engineer. Ever. I'd be impressed if you could even make it as a fucking technician.
>>16856096Why do these math facts make you so upset? Perhaps deep in your soil you recognize the problems.
That there are infinite natural numbers is the central property of infinity
>>16856082You could represent all of math just in the space between 0 and 1. Take degrees for example. If you have 180 degrees, that could just be 0.5. If you have one radian, that could be 1/(2*pi) = 0.1591549... If you have 27 degrees, that one would be 27/360 = 0.075 and so on. Whenever a problem asks to "find x", set the largest value to 1 and then x would be something between 0 and 1. Even if you want to calculate how much land you own, set the surface area of the entire earth to be 1 and then the area of your land would be something between 0 and 1, for example one hectare would be 0.000000000019562353. Everything and anything can exist in the interval between 0 and 1.
The definition of infinity is that it is something that is larger than any natural number
>>16859211Infinity only makes sense for sets, like the set of all natural numbers, not for individual numbers. This "larger" relationship needs a definition
>>16859221>what is "omega">what is "epsilon">what are transfinite cardinals and transfinite ordinalsI thought this board was for people that understood these things.
>>16854823>>16857503>>16859223>>16856082Take your meds math schizos.>There are an infinite number of blah blah... here's some Greek letters to make me feel validated and smartIf I can't count it on my fingers, it's not real.>Hi I'd like "an infinite fraction of infinities" of apples please.Said no one.Lol.
>>16856086>fucking AIhttps://youtu.be/FliNNOSKFPI
>>16859223>>what is "omega"The set of all finite ordinal numbers of course, but when anon wrote>The definition of infinity is that it is something that is larger than any natural numberIt doesn't sound like he's doing a definition of ω with the von Neumann order relation (an ordinal definition that needs the "axiom of infinity" to be fulfilled anyway), but rather like he's trying to define what an "infinity" of the ∞ kind is, taking natural numbers and the usual order as primitive, something which has nothing to do with the rest of the thread
>>16859286wtf does that song even mean
