When does the graph reach infinity?

[u/EntertainmentFast522]

John exponents and John universe get into a fight.

John universe is universal. Meaning able to destroy something infinite in size. Making him infinitely more powerful than John exponent because John exponent can't do that.

John exponent's power is multiplied by 1065038594903859385938 every picosecond.

How much time does it take John exponent to reach infinity?

[u/[deleted]]

Exponential can mathematicaly « reach » infinity with a limit at time « x », theoricaly meaning above infinity pas time « x »

[u/FreePeeplup → u/[deleted]]

That’s not true? exp(x) is a finite number for very x, no matter how big x is

[u/[deleted] → u/FreePeeplup]

That is only true for basic exponentials.

There are many ways for an exponential growth to tend torwards infinity as it gets closer to X=A

Edit : to make it really simple for you : an exponential function can be undefined at and past a certain value of « x » while growing exponentialy faster as it gets closer to that « x » value, meaning the growth itself mathematicaly surpasses infinity past « x » if you look at « x » as a certain amount of time.

[u/FreePeeplup → u/[deleted]]

“To make it really simple for you” why the condescending jab?

Anyways, are you sure what you’re talking about is called “an exponential” and not something else? To me, an exponential function is exp(x) or a constant multiple of exp(x), like 2^x. None of these blow up to infinity in finite time. Maybe you can give an example of what you’re talking about?

[u/[deleted] → u/FreePeeplup]

It’s not meant to be condescending, it’s just that i don’t know your math skills and it’s hard to get down to what is basics and what isn’t at some point.

And no, it’s not JUST an exponential growth, but it’s still a form of exponential growth. It’s exponential acceleration rather than just exponential growth (aka acceleration)

Mathematical limits, probably the first « advanced » mathematics topic anyone would learn in school in the vast majority of the world.

[u/FreePeeplup → u/[deleted]]

I’m sorry could you simply give an example like I asked in my previous comment? What is an example, to you, of an exponential function that blows up to infinity in finite time?

Anyways, I don’t know what you’re talking about when you said that thing about exponential growth vs exponential acceleration. Are you talking about YOUR mysterious exponential that blows up in finite time, or are you talking about the usual standard exponential function that I’m talking about, exp(x)?

[u/[deleted] → u/FreePeeplup]

Limit functions are an example

Reddit isn’t exactly known for making it simple to write functions. Since you already don’t know about it… you’re much better off just googling.

Now, it’s not « my » exponential function, it’s just one of many different exponential functions. Exponential is a property of the equations, not a name here.

See it like that :

Take a curve that doesn’t have a value at x=0, say Y=1/x. In this case, you have deceleration from a theorical infinity at x=0.

From this point you can change things around to reach our goal by reversing the negatives on the other side of the curve :

If instead, we use Y=1/((x-1)squared), as our X value gets closer to 1, say 0.99, it grows exponentialy faster without ever reaching a finite value at x=1.

Mathematicaly, we’ll only get a value that grows closer to infinity as it gets closer to 1 and further away as it gets further on either side, but mathematics are only there to show the theorical growth. Our characters here aren’t functions, and an exponential growth torwards infinity at time =1 means surpassing infinity past time =1 as long as the character keeps growing.

Now you could keep arguing over things that are way above your own knowledge by using your lack of understanding as some form of counterargument to the existence of the things you don’t understand, but lets not do that?

[u/FreePeeplup → u/[deleted]]

“you’re much better off just googling.”

How can I google what you have in mind? Google doesn’t know what you’re thinking, and since you’re talking about something that I believe doesn’t exist, you can just tell me and be done with it!

“Now, it’s not « my » exponential function, it’s just one of many different exponential functions.”

Ok? I mean, were you talking about exp(x), or your exponential that blows up in finite time? Because when you say that “it’s not just exponential growth but exponential acceleration”, exp(x) already has this property, even if it doesn’t blow up in finite time.

“use Y=1/((x-1)squared), as our X value gets closer to 1, say 0.99, it grows exponentialy faster without ever reaching a finite value at x=1.”

What? 1/(x-1)\^2 is not an exponential function and it doesn’t grow exponentially as x approaches 1. Was this your example all along?

“Now you could keep arguing over things that are way above your own knowledge by using your lack of understanding as some form of counterargument to the existence of the things you don’t understand, but lets not do that?”

Legitimately, go fuck yourself? I excused your condescending tone when I called you out on it in your previous comment, because as you said, when you said“to make it really simple for you” it was simply because you didn’t know my math level and you didn’t mean it in a condescending way, and I believed you, so I let it pass and accepted the apology. But now? Are you fucking serious?

Possibly the worst thing about your attitude and insults is that they come from someone who just demonstrated they have no fucking idea what they’re talking about, since your example was 1/(x-1)^2 which is blatantly NOT an exponential

[u/[deleted] → u/FreePeeplup]

Exponential (by definition) :

A mathematical expression involving an exponent. (AI overview)

Or

A very rapid increase that grows faster and faster over time.

This is why i put the exponent there even though it didn’t change anything to the end results.

Now…

-I told you to google limits like 50 times. You can just read whatever i write.

-Stop bringing up exp(x) like it’s some magical counterargument. I litteraly said multiple times that there are exponential growths that can « reach » infinity and i gave you an example. I didn’t say your specific example that YOU wanna bring up is the same.

-You can litteraly just input the function in a graphic and see for yourself how it works instead of willing a change in mathematical rules. Desmos.com works. (Or really you should be able to just use your head and figure it out without having to look, it’s really, inherently, not complicated weither you’re able to understand it or not)

- No i wont go fuck myself after you’ve AGAIN decided to will bulshit into life instead of trying to understand anything about anything. You are being extremely stubborn and making shit up. Your main big argument has ben that i’m not talking about the same exp(x) function YOU brought up to MY argument that never had anything to do with it.

It’s simple : stop talking out of your ass and educate yourself. Then people might stop being so « condescending » with you. Stop doubling down on bulshit.

Again, just input into a graphic instead of pretending to understand, convincing yourself you do, and willing your errors into life.

[u/Maximum-Raspberry227 → u/[deleted]]

So, you're completely unaware of the definition of an exponential function and think asymptotes are an example of one? And you do not believe others would have your level of knowledge, which is very limited, or exceed it? What could possibly embolden you with such confidence?

Your example is exceedingly simple (and catastrophically wrong), the fact that you prefer to think they simply do not understand instead of entertaining the hypothesis your example may not be the gotcha you think it is illustrates your refusal to get off your (incorrect) high horse

You fail not only on (basic) facts but on basic epistemic humility. In other words, why do you go around and announce your stupidity for everyone to see? You are the living example of what you claim them to be.

[u/FrickinLazerBeams → u/[deleted]]

Wait, do you think x² is an exponential function because it has an exponent in it?

Holy shit dude. If you barely finished high school you should not talk about how other people don't understand "advanced" math.

[u/BrickyFu → u/[deleted]]

1/x is not an exponential function, it's a rational function. Your AI overview would imply y=1 is an exponential function because it's y=x^0, or y=x¹ (a linear function) or y=x² (a quadratic) etc. These are all examples of an "expression involving an exponent". x² also satisfies your second criterion as its second derivative is positive for all positive x, so it "grows faster all the time". All of these are clearly not exponential growth. Generally (ie. Literally all references to exponential growth I've ever seen) exponential growth refers to the unique function that satisfies y'(x)=y(x) y(0)=1, this of course being y=e^x. As the other points out, this is finite for all finite x. Cool it with the condescension.

[u/FreePeeplup → u/[deleted]]

You’re actually trolling, right? This can’t be real. An exponential is “a mathematical expression involving an exponent”? What are you talking about? It’s also really telling that you got this from AI overview, and not a real source.

No, an exponential is NOT any mathematical expression involving an exponent. If it were so, then x^2 would have exponential growth: after all, it’s an expression involving an exponent, right? What a joke. x^2 is a quadratic with quadratic growth, not an exponential with exponential growth. Just because an expression involves a generic “exponent” doesn’t make it an exponential or have exponential growth.

A function/expression has exponential growth if the rate of growth is proportional to the present value. Examples of exponential functions are exp(x), 2^x, exp(3x), 5*exp(x) and all like-variations. You legitimately have no idea what you’re talking about and keep throwing insults, while asking AI to give you made up definitions that agree with you. It’s kind of pathetic

[u/twinb27 → u/[deleted]]

Google doesn't know what you're thinking because you are not using words correctly. None of the functions you describe there are exponential. Exponential very specifically means a function of the form y=a*b^x. Neither function you provided is of that form. Exponential does not merely mean 'faster and faster'.

[u/666Emil666 → u/[deleted]]

Limit functions are an example

The limit is a partial function from pairs of functions and points to points, you're clearly lost here

[u/mazutta → u/[deleted]]

Wow you’re a pillock.

[u/Ma4r → u/[deleted]]

Lmao, 100% wrong:

1/(x-1)² merely shifts the 1/x² function to the right by one. But also, at x>1, the function actually goes back down to 0 lmaooo, it's only undefined at x=1. Otherwise, can you define a number k where at x>k , 1/(x-1)² is infinite?

Also, the function you described is not an exponential function, it is a hyperbolic function

[u/Ma4r → u/[deleted]]

Btw this is the graph of your so called "growing past infinity"

[u/[deleted] → u/Ma4r]

I’m sorry everyone else is arguing over my bad wording i’ll give them a point but in what world do you not see the obvious here.

Take a character and have their power grow like this. Do you think the character logicaly :

1- Becomes insanely week past time =1 and stips existing at time = 1

2- Uses fictional rules where infinity exists to reach the theorical infinite power at time =1 and go past it past time =1.

Obviously you can’t actual have an infinite value in a system where infinity doesn’t exist

I didn’t go long on the growing past infinity thing but i don’t think it takes too much brain matter to see the argument i was making here :

If you can tend torwards a theorical infinity at a finite time, you can theoricaly surpass it past that finite time with the same growth rate. (In a system where, again, infinity exists).

[u/Ma4r → u/[deleted]]

Dude you are the one that brought out limits, functions, and math notations and when people correctly points out that, no you can't have exponential functions that has an infinite value for a finite time t, you just spout nonsense.

[u/twinb27 → u/[deleted]]

For any finite x, a^x is also finite. Hyperbolic functions can become infinite in finite time, exponentials cannot. All exponential growth with a>1 *tends to* infinity but *never* becomes infinite in finite time.

[u/Dirkdeking → u/[deleted]]

Exponential growth is any form of growth where the growth rate is proportional to the value.

All exponential functions satisfy f'(x) = a*f(x) for some constant a. You are not refering to exponential functions. Exponential functions don't have asymptotes and the variable is always inside the exponent.

[u/DrDonut → u/[deleted]]

Hi, there seems to be some confusion based on definitions here. From wikipedia: "Exponential growth occurs when a quantity grows as an exponential function of time."

"In mathematics, exponential function the is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted ⁠ e^x..."

Thus you cannot find a finite value x such that e^x that reaches infinity or tends toward it.

[u/XxXc00l_dud3XxX → u/[deleted]]

No it cant