>be first semester teacher
>get assigned real analysis to which im excited to teach
>explain how R is uncountable by hinting at different sized infinities as a precursor
>one of my students begins laughing before interrupting me saying"infinity is unmeasurable and therefore can not be considered to be bigger or smaller than another infinity"
>explain cantors diagonal argument, another 2 students begin whispering looking doubtful
>im visibly nervous now and start stuttering
>trying to get them to understand so i explain how a set of infinite numbers can be considered "bigger" if it has more subsets of infinte numbers
>the first student walks out, followed by another student shortly after
>majority of class now is skeptical of me and i dont even want to know how they will react next week when we go over cauchy sequences
how does one react to so much "doubt" they receive ? I thought the real numbers was settled science
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.011111111111111... and
.100000000000000... differ by every digit, but have the same numeric value. Cantor's argument is wrong because a single bit collision destroys the entire construction.
Cantor's argument uses binary sequences, not decimals. Have you even read it?
It uses the Schroeder - Bernstein Theorem moron to show that a bijection exists between both sets
>~~*Bernstein*~~
This is correct by compactness theorem
Its also bullshit.
1 = 2 according to the same logic.
Based copypasta poster
post the pasta, schizo
It's obviously a larp thread made by a falseflagging bergerschizo, note the "I thought the reals was settled science"
Sounds correct, youre teaching popsci-fi math, i would walkout aswell.
Did you remember to bring up how 6 million is basically the same thing as infinite?
kek
It’s nonsensical because it’s a fake abstraction.
There is no evidence that an infinite amount of anything exists in the real world.
How many times can you post this thread?
Skepticism is healthy and should be fostered and encouraged. The only issue is that you can't even be skeptic if you don't at least understand what the other person is talking about. Walking out of class as soon as one doesn't understand something simply outs that person as a brainlet. One should make an honest attempt at understanding the schizo theory of sets as entertained by Cantor and then humored by ZFC. Axioms are just that, axioms; and there can be no empirical evidence to prove or disprove that the rules of logic as we know it also apply to infinite objects, as we have no experience of infinity.
As shaky as its logical and intuitive basis may be, modern math has delivered plenty of results that "work", so let's go with that.
After your students get a math PhD they can join Wildberger and start criticizing modern mathematics while believing they have come up with better foundations.
perhaps its your delivery of the content, also if the content you presented isn't in the assigned textbook then skepticism arises. I always thought that Cantor's idea of different infinities wasn't that out of the ordinary if you think of bijective functions for finite sets. Hell, you can even think of functions which have the reals (0, 1) map to all the reals just as an intuitive exercise.
>if the students walk out, you probably did something in the past to upset them like have inconsistent grading criteria, act like an butthole or pervert, or just be unlikable somehow, to this regard its difficult to assist you
Is infinity the ultimate midwit filter in math? High IQ Chads can entertain the idea without any problems, while midwits constantly need to turn in into an infantile philosophy debate.
It would be nice if they were real, but it's time to admit that infinity like magic flying broomsticks from harry potter is not real.
>if it was REAL
Seems the frogposter was right
Abstract concepts such as infinity don't *exist* and aren't "real", just like the number 4 doesn't exist.
Whether you think our world has infinite processes is another discussion and one that is ultimately irrelevant to mathematicians.
Infinity is as valid of an idea as sadness, love, space etc, it all depends on the logical model in which you are arguing midwits can't grasp this for some reason (and with the axiom of infinity being foundational to literally every field of mathematics, I don't think there's an argument to be had as to its usefulness).
>heh u made an typo I winned
the intellectual maturity of "not infantile" infinitygays
Try to make your bait less obvious
>Is infinity the ultimate midwit filter in math?
no
that is conditional probability
Or naive set theory. A Chad mathematician will work perfectly with it, but a midwit will go on and on about Russell's "paradox" without seeing how it can be trivially resolved.
at a certain point it's all just wanking to get yourself off though. That point comes up when it stop being useful to reality.
>at a certain point it's all just wanking to get yourself off though. That point comes up when it stop being useful to reality.
Yes, that's basically when they introduce "solve for x" problems. Where do we ever need this?
>That point comes
...whenever a concept appears that pushes your working memory to its limit and challenges some convenient heuristic you can't do without.
aka it's an IQ filter
Two sets have the same size if every mapping between them that is an injection is also a surjection.
So the injection
f : N -> N
f(x) = x + 1
not hitting zero is a counterexample to the naturals having the same size as the naturals?
Exactly.
You're trying to sell them metaphysics when you should just be satisfied proving that there is no bijection between the reals and the naturals.
>>one of my students begins laughing before interrupting me saying"infinity is unmeasurable and therefore can not be considered to be bigger or smaller than another infinity"
>>the first student walks out, followed by another student shortly after
based PHD student trolling new lecturers by showing up in and leaving lectures in courses they are not even signed up for
The solution clearly is to ban them from campus and the rest of society so they can't spread their dangerous disinformation to others. We all remember the time the 1 != 0.999... cult grew too powerful and wound up accidentally nuking San Francisco.
It is obvious that you do not understand the subject that you got hired to teach.
This is the kind of situation the notion of "resigning" was created for.
OP you should remember when writing new stories on the Internet that people irl don't get up and walk out of the room, that happens in movies
>don't get up and walk out of the room
You've clearly never gotten a booty call in the middle of a lecture
>teaching class on set theory
>Thinking of ways to get the students interested
>Open mouth really wide to show excitement and fervor
>"GUYS!! there are so many types of infinity, even really big kinds like large cardinals. Inaccessible, mahlo, measurable, they go on and on!!
>Several students look at each other
>One moves his fist back and forth in the air like he's doing rock paper scissor
>One student raises his hand "So...this mahlo cardinal as you call it. they've proven it to exist?"
>"Uh well...no...it's like we ...well it's not proven because the axiom system we use can't show its existence"
>Student replies "Why are we talking about it then?"
>Another student asks me if the reals are a big cardinal
>At this point I get excited to talk about the continuum hypothesis
>"WE ACTUALLY DON'T KNOW HOW BIG THE REALS ARE!!"
>student says "so set theory can't tell us this? why do we still use set theory then?"
>Students all walk out in disgust
>My mouth is still open from the start
You could have told them that it is all in the holy bible. Then they would have just folded their little hands and absorbed anything.
>A zoomer complaining about woke zoomers.
OH NO WHAT ARE WE GOING TO DO AHHHHHHHHH.
END OF THE WORLD !!