/sci/ - Science & Math

[Anonymous No.11481067]

>there is more than one infinity
>some infinities are bigger or smaller than others
You realise that is just the exact same thing as what le trolly man is doing in this image, right?

[Anonymous No.11481130]

>>11481067
No, it isn't.

[Anonymous No.11481145]

>>11481130
What do you think [math]\omega + 1[/math] is?

[Anonymous No.11481167]

>>11481067
No, its not.
Lets assume c1 is a very very large number.
Lets define c2 as follows

c2=c1+1

Then....
c2-c1=1

c2-c1>0

c2>c1

But c1 is very large, as stated in the assumption. Therefore by convention, c2 is a bigger number than c1 i.e. c2 is an even larger number than c1.
Hence proved.

[Anonymous No.11481186]

>>11481067
>11481067
No it's not, because we actually PROVED that there exists different infinities. But just "adding 1" is not how you get them.

[Anonymous No.11481195]

>>11481186
>>11481145

[Anonymous No.11481196]

>>11481167
That's not how more than one infinity works.

[Anonymous No.11481200]

>>11481167
Infinity isn't a number though so that falls apart. Nothing is larger than infinity, I wouldn't even describe it as a value. You cannot achieve infinity, only approach it

[Anonymous No.11481903]

>>11481200
Well humans can't replicate it you mean only approach it. To approach something you have to concede it already exists

[Anonymous No.11482074]

>>11481067
Define "infinity" and "+".
>>11481145
Define [math]\omega[/math] and [math]+[/math].
>>11481903
Define "approach something."

[Anonymous No.11482079]

>>11481167
Get into maths, you seem to have that way of thinking

[Anonymous No.11482093]

>>11481067
What is cardinality

[Anonymous No.11482214]

>>11481167
Infinity isn’t a number though

[Anonymous No.11482259]

>>11481200
Infinity is just a placeholder for the concept “without end” or “gets larger and larger.” As you do x “to infinity,” y behavior occurs. There’s no sense in treating infinity as a size as if some infinities are greater. All sets of numbers without end, without limits, are unable to quantified, so none of them can be greater or less than each other, nor even equal to each other

[Anonymous No.11482856]

>>11482093
Define "cardinality"

[Anonymous No.11482873]

>>11482074
define u being a huge retard

[Anonymous No.11482918]

>>11482079
You mean retarded thinking?

[Anonymous No.11482947]

>>11482214
>>11481196
True. Infinity itself is more as a way for us humans to comprehend how big something is. It helps us escape from the fact that there's a number bigger than Graham's Number. We can just call that number infinity and go on with our daily work. But infinities are just mathematical concepts and don't really have much meaning in our universe. Yes infinities have types, but saying one infinity is bigger than the other isn't significant to our everyday lives nor to the universe.

>>11481186
True. But these infinities are bigger than some other infinities by some infinite amount. Maybe I should've wrote
c2=c2+C
Where C is very very large.

>>11482259
True. But the size of the real number set is bigger than the rational number set, bugger than integers and bigger than naturals. As you said infinity itself is a placeholder. We can keep it and forget about it.

I will end by saying that-
Infinity is both a value and a placeholder.

[Anonymous No.11482950]

>>11482214
>>11481196
True. Infinity itself is more as a way for us humans to comprehend how big something is. It helps us escape from the fact that there's a number bigger than Graham's Number. We can just call that number infinity and go on with our daily work. But infinities are just mathematical concepts and don't really have much meaning in our universe. Yes infinities have types, but saying one infinity is bigger than the other isn't significant to our everyday lives nor to the universe.

>>11481186
True. But these infinities are bigger than some other infinities by some infinite amount. Maybe I should've wrote
c2=c1+C
Where C is very very large.

>>11482259
True. But the size of the real number set is bigger than the rational number set, bugger than integers and bigger than naturals. As you said infinity itself is a placeholder. We can keep it and forget about it.

I will end by saying that-
Infinity is both a value and a placeholder.

[Anonymous No.11482954]

>>11482856
>>11482093
Cardinality means the number of elements in a set.

[Anonymous No.11482961]

>>11481200
inf is larger than R
inf is unbounded

[Anonymous No.11482965]

>>11482259
>“gets larger and larger.
no, inf isn't a diesel engine chugging along

[Anonymous No.11482991]

>>11482954
Define "number", "element" and "set"

[Anonymous No.11483006]

>>11481067

The fact that retards can seriously talk about "infinities" illustrates just how much of a cult maths has become. The fact that the same tards will vehemently defend such absurdities demonstrates how much of a dogma maths has become. At this point its more like a religion than a rigorous discipline.

[Anonymous No.11483011]

>>11482950

An absolutely boomer tier answer. Thanks for the insight into how your mental midget mind works

[Anonymous No.11483028]

>>11482991
Is English your first language? Are you some tribal retard who doesn't understand a simple English sentence?

[Anonymous No.11483032]

>>11483011
The fact that you replied in a non discussion worthy manner, speaks volumes about your mental capacity. Rather than calling me a midget, try to point out the flaws in my reply. Looks like you're a retard who couldn't take in a word that I wrote.

[Anonymous No.11483034]

>>11481067
Larger infinities follow directly from the existence of the real numbers. Arguing against different cardinalities of infinity implicitly contradicts the existence of a "continuous" number space. You can make this argument if you want, but it's not trivial or obvious

[Anonymous No.11483048]

>>11483006
Retards like Wildberger like to use nonsensical expressions such as "infinities", to set up their anti-mathematical strawman arguments.

[Anonymous No.11483062]

>>11482093
>>11482856
>>11482954
The cardinality of [math]A[/math] is the equivalence class of [math]A[/math] under the equivalence relation "equal cardinalities" (the existence of bijections).
>>11482214
There is no such thing as "a number", but you are correct that infinity is not a real number.
>>11482259
>Infinity is just a placeholder for the concept “without end” or “gets larger and larger.”
This is only somewhat correct in the sense of analysis, where the symbol [math]\infty[/math] comes up in limit notation as syntactic sugar, but even then, limits are actually rigorously defined. [math]\lim_{x\to\infty} f(x) = L[/math] is just fancy notation for the formal statement [math]\forall\epsilon(\exists N(x > N\implies|f(x)-L|<\epsilon))[/math] where [math]\epsilon[/math] is a positive real number and [math]N[/math] a positive natural number, and [math]\lim_{x\to c} f(x) = \infty[/math] is just fancy notation for the formal statement [math]\forall M(\exists\delta(0<|x-c|<\delta\implies f(x)>M))[/math] where [math]M[/math] is a positive natural number and [math]\delta[/math] a positive real number. (In fact, for that second statement, it is more accurate to just say "[math]\lim_{x\to c} f(x)[/math] is undefined.")
In the sense of set theory, which is what people are actually talking about when they talk about "infinities" (cardinalities of infinite sets), you are incorrect. "Infinity" here is a cardinal number, usually [math]\aleph_\mathrm{whatever}[/math], but NEVER EVER [math]\infty[/math].
>>11482873
Brainlet.
>>11482950
>It helps us escape from the fact that there's a number bigger than Graham's Number.
There are uncountably infinitely many real numbers greater than Graham's number.
>infinities are just mathematical concepts and don't really have much meaning in our universe.
Define "meaning."
>>11482991
>Define "number"
No such thing. Cardinal numbers exist, however, and are rigorously defined.
>"element" and "set"
Depends on your axioms.

[Anonymous No.11483067]

>>11482950
>but saying one infinity is bigger than the other isn't significant to our everyday lives nor to the universe

We use this fact everyday when you work with real numbers

[Anonymous No.11483070]

>>11482950
Smoothbrain tho

[Anonymous No.11483072]

>>11482074
Based

[Anonymous No.11483073]

>>11482991
Define "define"

[Anonymous No.11483209]

>>11483062
>There are uncountably infinitely many real numbers greater than Graham's number.
There are infinitely many infinities greater than infinity. My earlier statement was made considering all the brainlets in mind.

>Define "meaning."
Our universe only has a finite amount of anything. True infinity doesn't exist in our universe. Nothing is infinitely heavy/large.

[Anonymous No.11483225]

>>11481067
There is only one infinity.

Just like there is only one up. You cannot go up up, you either went up or you didn't. All the locations considered up are all still up. There is no way to be larger than infinity.

[Anonymous No.11483234]

>>11483225
>Just like there is only one up
No. Your definition of UP is relative. In fact its relative to the frame of reference on the earth. There's no absolute UP.

[Anonymous No.11483237]

>>11483209
>There are infinitely many infinities greater than infinity.
Define "infinity."
>Our universe only has a finite amount of anything.
Pick two points in space. How many points are between them?

[Anonymous No.11483250]

>>11483237
>Define "infinity."
Are you the guy I replied to?If no, then eat your coom to get enlightened.

>Pick two points in space. How many points are between them?
Those are abstract objects. Use common sense.

[Anonymous No.11483265]

>>11483250
>Are you the guy I replied to?
Yes. I've asked twice now and I notice you still haven't defined "infinity," so I shall implore thrice: define "infinity."
>Those are abstract objects. Use common sense.
What is your point?

[Anonymous No.11483285]

>>11483225
>There is only one infinity
depends on definition

[Anonymous No.11483295]

>>11481067
No.
"Bigger" or "smaller" infinities are something you arrive at after defining cardinality thru a bijection.
Basically using a pigeonhole argument.
For example for every ration you can have a natural number, but doing the same with say the reals is impossible.

[Anonymous No.11483320]

>>11482954
>>11483062

These posts are correct.

Assuming that by infinity it is meant the set of all natural numbers, Infinity plus one is the same cardinality (size) as infinity as a bijection (one to one match between each element in both sets) exists.

The are however other infinite sets (such as the real numbers) where no bijection is possible - lookup Cantor's diagonal proof. Therefore the real numbers have a higher cardinality than the natural numbers.

The ordinality (order) of "infinity plus one" is more than "infinity", this does not mean it is a bigger number, just the next one.

In the comic, the main character said "highest" - if by this he means "biggest" he is talking about Cardinality and Troll Dad is wrong (though there are larger infinities). If however by "highest" he means "last number" he is talking about ordinals and Troll Dad is right.

[Anonymous No.11483336]

>>11483265
>Yes. I've asked twice now and I notice you still haven't defined "infinity," so I shall implore thrice: define "infinity."
I don't know if you're trolling or truly retarded as fuck. Then define "define" you dumbass bitch. I still don't understand why you're trying to ask such a trivial question when you can google this shit.

>What is your point?
Speaks volumes on your intellectual capabilities. pic related.

I'm willing to explain non trivial concepts such as 'abstract points' but I refuse to explain dogshit words like 'infinity', 'set', 'cardinality'. So either stop asking and go suck your mom's tits because you're clearly underdeveloped or have a civilized scientific discussion here.

[Anonymous No.11483339]

>>11483320
People here are retarded as fuck by not understanding such trivial concepts. Makes sense that 4chin is filled with NEETS and brainlets.

[Anonymous No.11483342]

>>11483265
For the purpose of the comic, infinity is the cardinality of the set of all natural numbers.

[Anonymous No.11483424]

>>11483336
>Then define "define" you dumbass bitch.
Primitive notion.
>I still don't understand why you're trying to ask such a trivial question when you can google this shit.
Because I'm trying to get you to fucking think, which you clearly haven't done at all at any point in this thread, you fucking retard. If it wasn't clear yet, "infinity" has different meanings depending on the context, and you, cheating weasel you are, have been using them interchangeably and then sobbing like a woman about how complicated the "concept" is for your chimp brain, so I am asking you to settle on one goddamn definition for the ambiguously defined idea you're pretending to attempt to discuss, which is pretty much common sense that you unlock when your IQ reaches 2 digits. I'd call you a fraud for your intellectual dishonesty, but you might actually be such a windowlicking spastic that you don't even realize how much of a coward you are. You utterly contemptible little worm. You dipshit. You fucking child.
[math]\epsilon[/math]/10 made me reply

>>11483342
Sure. For the purposes of the comic:
>There is no highest number because there is no such concept as "a number."
>There is no highest natural number because [math]n\in\mathbb{N}\implies(n+1)\in\mathbb{N}[/math].
>There is no highest real number because of the Archimedean property.
>There is no highest complex number because the complex numbers cannot be ordered.
>If infinity is [math]\aleph_0 [/math], then infinity + 1 is undefined because [math]\aleph_0 +1[/math] is undefined.
Onto the retarded OP's post:
>If "infinity" refers to the cardinality of an infinite set, then there is "more than one infinity" because [math]\mathbb{N}[/math] and [math]\mathbb{R}[/math] are infinite sets with two different cardinalities.
>Since there is an injection from [math]\mathbb{N}[/math] to [math]\mathbb{R}[/math] but not vice versa, [math]|\mathbb{N}|<|\mathbb{R}|[/math] by definition of cardinality.

[Anonymous No.11483442]

>>11481067
>The people on this board calling you stupid haven't even taken topology
Really makes you think

[Anonymous No.11483455]

>>11483424
Where the fuck am I sobbing like a bitch. Let me enlighten you on all the posts I've made on this thread.
>>11481167
>>11482918
>>11482950
>>11482954
>>11483028
>>11483032
>>11483209
>>11483234
>>11483250
>>11483336
How much you wish to trust that I've made these posts as a matter of fact, is all up to you. I'm truthfully laying it in front of you.

>"infinity" has different meanings depending on the context
Yep. I don't deny it. Infinity in limits, calculus is not the same as in number theory. The infinity that I've been talking about in my posts is in regards to number theory, since OPs question is more number theory related.

>which is pretty much common sense that you unlock when your IQ reaches 2 digits.
Pretty accurate.

[Anonymous No.11483469]

>>11483424
>I'd call you a fraud for your intellectual dishonesty, but you might actually be such a windowlicking spastic that you don't even realize how much of a coward you are
I'm not dishonest neither a coward. I assumed since the current topic of infinity is clear because of OPs post, you were just asking retarded questions. I didn't think my post were equivocating.

[Anonymous No.11483498]

>>11483455
>Where the fuck am I sobbing like a bitch.
"Math is retarded because I can't understand it", "we can't really know infinity." Despite the fact that there are rigorous definitions for every usage of the term "infinity" depending on the context. But perhaps I am being uncharitable.
>>11483469
>I assumed since the current topic of infinity is clear because of OPs post
The OP is unclear. It attempts to draw some equivalence between basic set theory and "Infinity + 1", which does not make sense in the real numbers or the cardinal numbers (but could make sense in the ordinals). Of course, it's a troll, so that's the whole point.

[Anonymous No.11483501]

>>11481067
read Hegel

[Anonymous No.11483527]

>>11481067
2/0= infinity
1/0= infinity

2/0 > 1/0
One infinity is bigger than the other.
If we can figure out a branch of math that allows reversible division by zero, the question of "different infinities" could be resolved

[Anonymous No.11483550]

>>11481200
you cannot approach infinity. the largest real number you can imagine is still no closer to infinity than 0 is.

infinity is simply, straight-forward, flat-out, not a number. at all.

it has nothing to do with numbers. it has no relation to numbers.

[Anonymous No.11483563]

>>11483498
>Math is retarded because I can't understand it
>we can't really know infinity.
Not even once did I call math retarded. Yes, I've said that infinities are ambigous primarily because there aren't well defined in one specific context.
Ex what is the value of infinity? There's no answer. But we do know the value of Graham's number which makes G's no definitive and finite and still infinitely smaller than infinity.

> It attempts to draw some equivalence between basic set theory and "Infinity + 1"
I ignored OPs photo, since most posts on 4chin have useless photos. Yes there's no relation, since set theory is not the same as pure number theory.

[Anonymous No.11483594]

>>11481067
Not really. The existence of different types of infinities is demonstrated by the fact that we can show there exists no bijective correspondence between infinite sets. The algebra of infinite sets involves more care regarding cardinals and ordinals, but the most basic thing you have to understand is that the most natural way to “add one” to infinity is to take a power set. Cardinality tends to be a very robust property of sets, but one of the ways we know how to break through it is the power set operation.

[Anonymous No.11483607]

>>11482074
Define "define".

[Anonymous No.11483610]

>>11483594
>can't even prove infinity exists
>immediately assumes multiple cardinal infinities exist
smoothbrain

[Anonymous No.11483612]

>>Lets imagine infinity exists
>>Now lets imagine infinities exists
>>Lets imagine green talking rabbits breathing water and reciting Plato. Because we can.

The state of mathematics.

[Anonymous No.11483617]

>imagine infinity exists
>imagine a number so large that it approaches infinity
>imagine a number growing legs and walking around on it's own so that it may approach things

[Anonymous No.11483634]

>>11483617
fish evolved legs why can't numbers

[Anonymous No.11483635]

*Zeno's paradoxically*

[Anonymous No.11483637]

One day these imbeciles who blather away about their imaginary infinities are going to be called to God's judgement. Verily they shall be cast down into the ETERNAL torments of HELL! BY GOD! TO BURN! FOREVER! IN ETERNAL TORMENT!

ETERNAL!!!!!

..wait

[Anonymous No.11483647]

>do 3 steps of solving an equation
>tag "+ ..." onto the end of it
>"assume we have done infinite work and come to the correct result"

[Anonymous No.11483661]

>>11483637

Alright, Obviously it cant be ETERNAL torment. Because infinity doesn't exist. So we have to come up with another way to deal with this and make sure those Infinity SINNERS are adequately punished in the afterlife.

FINITE TORMENT! Yea, and so they shalleth be cast into the FINITE fires of HELL to burn for a FINITE...

Damn, it just doesn't carry the same impact as ETERNAL torment, does it? Back to the drawing board.

[Anonymous No.11483683]

>>11483661
Infinity exists. Infinity doesn't exist as a number concept, however. Galileo himself rationalized that nothing is greater, less than, or even equal to infinity.

When you go to hell for believing in your false infinity, your eternal torment will not have a number relative to the amount of time you spend there attributed to it.
Alternatively, you'll have all the time you could ever want to infinitely add numbers into the set of all real numbers, one by one.

[Anonymous No.11483684]

>>11483563
Do you finally have the answer that you required from me?

[Anonymous No.11483692]

>>11483661
So, I have given this careful thought and concluded that we need a number so large that it may as well be infinity, but its finite and nothing is bigger. I have decided to all this entity "the motherfucker of all numbers" and its defined as being the biggest number and no smart ass can add shit to it.

"Yea, and so the infinity SINNERS were called unto God's presence upon JUDGEMENT day and there was a great gnashing of teeth as they quailed before the feet of the ALMIGHTY. Thusly they were CAST down into the fiery depths of HELL to burn for THE MOTHERFUCKER OF ALL NUMBERS!

What do you think guys? I think I have nailed it. Sure shown those infinity freaks. Their fancy pants hocus pocus will not save them now.

[Anonymous No.11483697]

>>11483610
What do you mean by “exists?” Under the construction of the natural numbers, I can show there exists no greatest element, and thus by succession I can produce arbitrarily large unique naturals. Using this result, one can show it would be impossible for there to be a finite amount of unique naturals.

[Anonymous No.11483731]

>>11483697
>I can show there exists no greatest element
so infinity doesn't exist as a greatest element, good.

you're also providing evidence for how pointless the topic is
>one can show it would be impossible for there to be a finite amount of unique naturals.
this assumes that without proving as much, that there must be finite amount in lieu. Why?
Taking your desire away of trying to prove a largest natural can't exist, doesn't suddenly mean a largest natural exists and that you have to prove what it is.

In truth, for any given application of real math producing a real result in the real world, there is a finite end to anything that would otherwise "appear infinite". You don't need a trillion digits of pi (much less infinite digits) to launch a rocket into the orbit of jupiter.
You don't need 30 decimal places of accuracy to determine the length of something measured within an inch using a 12 inch ruler.

>one can show it would be impossible for there to be a finite amount of unique naturals.
no, one can not "show it". They can merely assume it, and then do everything possible to try avoiding actually "showing" it because the implication of the infinite work required to do actually "show" it is incomprehensible.

[Anonymous No.11483848]

>>11483731
what the fuck kind of argument is this?
btw, there ARE an infinite amount of particles in space, space is infinite.

[Anonymous No.11484032]

[Anonymous No.11484062]

Just stipulate that "infinity" is the name of the number x such that there is no other number n such that n>x.

[Anonymous No.11484092]

Let N be the set of natural numbers and T the set of multiples of 10:

N = { 0, 1, 2, 3... }

T = {0, 10, 20, 30... }

N and T are both obviously infinite. However, while every element in T is also in N, the reverse is not true, meaning that N is larger than T.

[Anonymous No.11484118]

>>11484092
this is not how we measure size, silly

[Anonymous No.11484134]

>>11484092

Two sets are equal if a bijection is possible between them. Each n in N can be matched with each n in T by matching each number to its multiple. So the sets have the same cardinality or size.

[Anonymous No.11484146]

>>11483731
>infinity doesn't exist as a greatest element
infinity isn't an element of the set...
It seems you're either an engineering student or a schizo like zeilberger and wildburger.
I'd respond in good faith, but that's more or less a waste of time if you're concerned with the applications of math (which is fine) rather than any pure mathematics.

[Anonymous No.11484151]

>>11484062
infinity isn't a number. We can't reason with it as though it were a number - mathematics involving infinity is generally much more careful than that. Otherwise, there's no subtlety between a mere upper bound and actual infinity, and we wouldn't be able to reason about different infinities.

[Anonymous No.11484157]

>>11484092
No. When you reason with infinite cardinalities, it subset inclusion doesn't mean there are 'fewer' objects in the subset. If there exists bijective correspondence between the elements of both sets, then they have the same cardinality. An uncountably infinite set (say, the reals) can have both countably infinite (rationals) and uncountably infinite (the irrationals) subsets.
All subsets give you is that the set containing them must be at least the cardinality of the subset

[Anonymous No.11484159]

There are an infinite amount of particles in the universe

[Anonymous No.11484167]

>>11484159
No there aren't.
there are only like 1.8×10^64 amounts of cubic planck lengths in the entire volume of the universe.

[Anonymous No.11484173]

>>11484167
known universe
the actual universe is infinite

[Anonymous No.11484182]

>[1, 2, 3, ...] = the set of all integers
>there are infinite numbers in there dude just trust me
nigga you wrote 1,2,3 infinity
Are you for real nigga
lmao who do you think you're fooling.
Why'd you stop at 3. Go on, keep putting "all the integers" in the set. Prove the set contains all the integers by actually writing out all the integers.

lmao nigga

[Anonymous No.11484206]

>you're allowed to put a closing bracket AFTER instantiating the set of all numbers and claim it contains infinite elements
>But you're NOT allowed to put another number AFTER an infinite repeating decimal like {0.000...1}
pick one or the other, mathfags.

[Anonymous No.11484230]

>>11484092
Thanks to my new and amazing conceptual breakthrough in some theory, we now have "THE MOTHERFUCKER OF ALL NUMBERS" ( MFOAN) to replace that blasphemy otherwise known as "infinity"

See >>11483692

So I will fix your heresy so you do not burn in a finite Hell.

Let N be the set of natural numbers and T the set of multiples of 10:

N = { 0, 1, 2, 3... MFOAN }

T = {0, 10, 20, 30... MFOAN }

N and T are both obviously finite. However, while every element in T is also in N, the reverse is not true, meaning that N is larger than T, as it damned well should be.

There! Fixed! I saved another soul from MFOAN damnation in the fires of HELL!

[Anonymous No.11484241]

>>11484206

Both the set of all natural numbers and the decimal expansion of a number are infinite.

Neither the set of all natural numbers nor the decimal expansion of a number contain a last element/digit

So there is no contradiction.

[Anonymous No.11484269]

>>11484241
Can't use a closing bracket on an "infinite" set. That bracket would have to come after an infinite expansion of elements.

[Anonymous No.11484297]

>>11484269

The closing bracket does not come "after" the elements of a set, except typographically.

[Anonymous No.11484316]

>>11484297
The last digit of an infinitely repeating decimal does not come "after" the infinite repetition, except typographically.

Pick one or the other. Either things can exist after infinity or they can't.

[Anonymous No.11484322]

>>11481067
Math. Singular. Retard

[Anonymous No.11484382]

>>11484322
>Physicalities
>Physics
>Schematics
>Schemes
>Mathematics
>Math
Why are Americans so retarded?

[Anonymous No.11484495]

>>11481167
>Hence proved.
What is proved? Someone please explain what this anon thinks he has proved here. Is it
>c2>c1 therefore infinity+1 is possible
? Your stupidity annoys me. Fuck you.

[Anonymous No.11484500]

>>11484382
>proved
>proven
Fuck I feel like I've betrayed my country.

[Anonymous No.11484835]

>>11483424
>Primitive notion
Define primitive notion you dumbass bitch.

[Anonymous No.11484849]

>>11482074
This inspires me to name the demanding definition ad nauseam fallacy. btw I hate fucking idiots that use this to deflect under the pretense of participation in the discussion. You should define death by empirical observation.

[Anonymous No.11485142]

>>11484835
"A primitive notion is a concept that is not defined in terms of previously defined concepts." An example would be a point in Euclidean geometry or a set in ZFC.
See, the difference is that you can just Google this and get an unambiguous answer, but "infinity" and "addition" have various different meanings that you and the rest of your retard ilk have been using interchangeably ITT, you braindead spastic.
>>11484849
It's not deflection. No "discussion" can even be had about a concept if every participant has a different idea of what that concept even is. Of course, if you're retarded (and you specifically are), the notion "Nobody in a conversation should be retarded about what they're talking about" is an attack on you, so I can see why you'd take it personally. You retard.

[Anonymous No.11485716]

>>11481067
It's threads like this that make me wonder if /sci/ isn't mostly retards. I've seen more intelligent discussions on boob physics on 4chan than this.

Countable infinity, is the basic notion of infinity, with the natural numbers being the baseline. If you can set up a 1 to 1 correspondence to any set of infinite numbers then that set has the same size of infinity.

The infinity of all real numbers is strictly larger than the infinity of the integers, because no 1 to 1 correspondence is possible.

It is possible to get larger infinities however. The basic idea is the power set, which is the set of all possible subsets of a chosen set.

So, the set of all possible subsets of the real numbers has a degree of infinity that is strictly larger than the set of all real numbers.

You can look up proofs for these ideas if you're not convinced, but I'm not wasting my worthless time trying to convince any of you.