Do we all agree on these?
∞ + 1 ≠ ∞
∞ - 1 ≠ ∞
∞ / 1 = ∞
∞ * 1 = ∞
>>7989597
>implying you can perform arithmetic operations on infinity
underage pls go
>>7989597
No.
>>7989597
What do those first two equal then, if not infinity?
>>7989613
∞ + 1 = ∞ + 1
∞ - 1 = ∞ - 1
infinity is a direction not a finite number
>>7989625
never implied that it was a finite number
>>7989620
>∞ - 1
while ∞ + 1 makes perfect sense (see ordinals), ∞ - 1 makes absolutely none (axiom of foundation prohibits shit like that)
>>7989620
You are using ∞ as an unknown, I don't think that's how it works.
>>7989635
∞ + 1 > ∞
>>7989628
You did when you tried to use every single one of those operators
>>7989648
i don't see a problem with the op, care to elaborate?
>>7989620
why do ∞ / 1 and ∞ * 1 equal ∞ and not ∞ / 1 and ∞ * 1 then?
>>7989650
You don't see the problem with algebraically manipulating an innumerable quantity?
>>7989647
Nice trick, but ∞ is not a real number and also it doesn't work like any other number in arithmetic. So ∞ + 1 = ∞. ∞ continues ∞, don't matter how much are you adding to it.
>>7989654
it's one infinite number. you have 1 infinity.
1∞ = 1∞
2∞ ≠ ∞
∞/2 ≠ ∞
2∞ = 2∞
∞/2 = ∞/2
>>7989656
i see it as 1 innumerable quantity, which means that if i subtracted 1 number from that quantity, it would be itself minus 1.
>>7989667
Now I know you're either trolling or in high school
>>7989663
Any arithmetic you do to infinity just results in infinity, you cant make it bigger or smaller
>>7989671
(You)
>>7989672
>∞ - 1 ≠ ∞
>>7989689
>>∞ - 1 ≠ ∞
Sure it does
∞ - ∞ is the one that isn't defined
>>7989700
∞ - ∞ = ∞ - ∞
>>7989705
> implying
>>7989689
∞ - 1 = ∞
Whether you like or not
>>7989597
>∞ + 1 ≠ ∞
>∞ - 1 ≠ ∞
No, that's not how it works. An infinite quantity plus or minus any finite quantity is still an infinite quantity.
Just as you can't count up to infinity, you can't count down from infinity, or up past infinity.
>∞ / 1 = ∞
>∞ * 1 = ∞
Yes. An infinite quantity divided or multiplied by a finite number is still infinite.
if n is a finite number, then:
∞ + n = ∞
∞ - n = ∞
∞ / n = ∞
∞ * n = ∞
>>7989777
Finally someone with fucking sense.
>>7989597
sqrt1*∞ = one third
PROOF THAT FRACTIONS ARE FUCKIN WACK
>>7989777
∞ + n = ∞ = ∞ / n
∞ - n = ∞ = ∞ * n
I thought you guys were supposed to be uni grads this is baby picture logic
>muh torus
btw, with these tools, induct the formulas of n to these parameters and take us to one of these fresh proto planets
DO IT
>>7989777
Infinity/0 is undefined
Infinity*0 is 0
Checkmate
>>7989800
Nope
> ∞ / 0 = ∞
> ∞ * 0 is undefined
>>7989803
Pretty sure both are undefined because all over zero is undefined and nothing times everything is paradoxical, leading to being undefined again
>>7990113
If we're already allowing operations on inf, we can allow x/0 to be inf for positive x and -inf for negative x.
>high schoolers think infinity is a number
Shake my head to be honest family
Either that or its more of that
>I was only pretending to be retarded
bullshit
>>7990141
https://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations
∞ + 2 = 43% Burnt
>>7990143
Extended real numbers are only used by applied math cucks
>>7990164
Like....Rudin?
>>7990164
they're used all through analysis newfriend. ordinal arithmetic is also a thing.
you don't know anything do you?
>>7989597
Saged, infinity isn't a fucking symbol you can do what you please with.
>>7989605
What is the extended complex plane
>>7989597
Nope. The first two are not true. Look up extended complex plane
>>7989597
∞ = philosophical concept, NOT mathematical or scientific
>>7992216
Math is a form of philosophy, every number is a philosophical concept
>>7992242
Do you understand Bertrand's essay on Numbers, then? I fucking don't.
>Be Russel, be smart
>Write essay explaining numbers
>Explain why you can't use counting to explain numbers
Well shit, Russel. Now what do we do?
>>7992249
Math is totally self-referential, numbers mean whatever you define them to mean. All the interesting shit comes when you try to be consistent in your definitions, and the emergent properties that occur from that
>>7992260
what if we create another formal system with cuter axioms, could it be that they create a more useful or interesting results than current math?
>>7992242
How much do my unicorn dreams weigh?
>>7992287
>only interesting
w-why not useful?
>>7992304
Because if your axioms arent based on something that reflects reality your math probably wont be applicable to reality either
>>7992308
t-thanks senpai.
Although we could create some absurd rules and from that construct and see what happens, we might find something interesting we could then apply to math
>>7992347
Possibly, it would be fun if nothing else, and i'm sure you could spin it into some pretty art
>>7992358
what about set theory?
A person create some nerd bs and now it's quite good.
T-helper 1 cells can activate macrophages. Does that mean T-helper 2 cells can doubly activate double macrophages?
This is what you sound like when you treat infinite like an algebraic quantity.
>>7992365
Wasnt set-theory an attempt to justify the axioms already in use? And then it lead to new branches of math because of the implications?
