@@sherueatyourbestfriend6791 Learning makes everyone happy and being proud of it makes sense..instead of eating your best friend,you better learn how to appreciate even small things in life:)
The thing I don’t get about epsilon-delta proofs is the “choose” part, I can’t understand how I have to choose, is there a formula for the right answer or what?
In my experience of getting a minor in mathematics, epsilon delta proofs of limits only really comes into play later in the upper level classes. The first time I looked into them in detail was Real Analysis. This was after calcs 1-3, Linear algebra, and abstract algebra.
@@gregsavitt7176 could i ask the reason for formalising such concepts? I mean i know it's standard practice to have everything rigorously defined, but is That really necessary?
@@Qrudi234 To answer your question, yes it is, but not for exercices like this video and very rarely for computation purpose. I see 2 reasons. 1) It is necessery to have a proper limit definition in order to generalize limits to metric space as they are often not as intuitive and 2) at some point, results in analysis are not as trivial and need epsilon argument to properly prove them.Just to name a few, results tied with Cauchy sequence, uniforme convergence, compactness and completeness often need such argument (but not necessarily in more general topologycal context, but that's another story).
bro I know how to get simple definite and indefinite integrals. by simple i mean something like no fractions or trigonometry in the equation but still while solving it it can have trig
I HATE THE EPSILON DELTA DEFINITION OF LIMITS I HATE THE EPSILON DELTA DEFINITION OF LIMITS I HATE THE EPSILON DELTA DEFINITION OF LIMITS I HATE THE EPSILON DELTA DEFINITION OF LIMITS I HATE THE EPSILON DELTA DEFINITION OF LIMITS
Do you want to know the dark side, where you can just show that if x is infenitesimaly close to 2, then 3x-1 is infenitesimaly close to 5 and it will be formall proof? Take d -any infenitesimal f(2+d)=3(2+d)-1=5+3d≈5 qed
He is not really choosing it to be that. For an epsilon-delta proof you need to show that for any given epsilon there exists a delta (both positive), such that the statement 0
I finally understand this. Delta is a function of epsilon such that an infinitesimal rectangle with epsilon and delta as the legs can contain all points a distance dr away from the point in question. If this rectangle exists than we say the limit exists. This usually fails if for some small length epsilon the delta length is cut short from some singularity that is contained in the small rectangle.
It's the formal definition of a limit. In the first method, he just plugs in x=2, and evaluates the expression to find the limit as x approaches 2. For this example, it's just a simple linear function, and we have no discontinuities, so there's no need to do anything more than that to find the limit. The second method formalizes the process, in what we exactly mean by "approach". Send x arbitrarily close to 2 without being 2 exactly. Does (3*x-1) continue to get closer to 3*2-1, as x approaches 2? That's what he's calculating. They call it the epsilon-delta proof, because epsilon and delta (the Greek equivalents of e and d) are the traditional symbols that are used for this process.
The epsilon delta definition of the limit is a hell of a lot more intuitive if you first teach kids the definition of the limit of a sequence. That intuition is enough for the form of the epsilon-delta proofs to make sense, but in the war against number theory unfortunately sequences aren't taught in school.
Adult calculus: largely irrelevant and unnecessary for normal use, making the intuitive version more complicated and time consuming. Ig that says something about being an adult lol
Gigachad using nonstandard analysis take any z≈2, let's say 2+epsilon for some arbitrary epsilon - infenitesimal. Then 3z-1=6+epsilon-1=5+epsilon≈5 Hence the limit is 5
it's very easy to show x is continuous and then use limit laws to show all polynomials are continuous. anybody doing math at a higher level would just plug in x=2
𝔸𝕀 ℂ𝕒𝕝𝕔𝕦𝕝𝕦𝕤 To solve the limit \(\lim_{{x \to 2}} (3x - 1) = 5\) with step-by-step explanations, let's follow these steps: 1. **Understand the expression inside the limit**: The expression we are dealing with is \(3x - 1\). 2. **Substitute the value \(x = 2\) into the expression**: Since we want to find the limit as \(x\) approaches 2, we substitute \(x = 2\) into the expression \(3x - 1\). \[ 3(2) - 1 \] 3. **Perform the arithmetic**: Calculate the value of the expression after substitution. \[ 3 \cdot 2 - 1 = 6 - 1 = 5 \] 4. **State the limit**: Since the expression \(3x - 1\) is a linear function (which is continuous everywhere), the limit as \(x\) approaches 2 is simply the value of the function at \(x = 2\). Therefore, \[ \lim_{{x \to 2}} (3x - 1) = 5 \] Thus, the limit is \( \boxed{5} \).
Teenage Calculus: check that the function is not to be able to be evaluated + not continuous near the target value before using the epsilon-delta definition
Honestly;y I wish epsilon delta proofs were taught in calc, I still don't really get how they work and I'm towards the end of my 2nd year as a math major.
Calc 3 and Differential Equation RN, and I still hate doing anything to do with limits and the summation symbol. JUST LET ME DO INTEGRALS AND DERIVATIVES
![DDG & G Herbo - Nosey [Official Video]](http://i.ytimg.com/vi/I9Ra0Zc2NlQ/mqdefault.jpg)
Baby calculus: in class
Adult calculus: exam
its literally the opposite bro
I agri
@@w8floosh281Only if ε > 0 though.
😂🤣😂🤣
And that was a ‘simple’ epsilon-delta proof😭
Thankfully, they removed them from the AP exam.
@@primoop9881 Wow, I didn't realize that they had them on the exam at one point. That would be pure pain.
delta eplsion proofs are so henious
It means that they didn’t think you could do it. But you can, in fact, do it.
I am just happy cuz I understood what you did and I could do that too if I wanted to.
That's not something you should be proud of tho
@@sherueatyourbestfriend6791 Learning makes everyone happy and being proud of it makes sense..instead of eating your best friend,you better learn how to appreciate even small things in life:)
@@sherueatyourbestfriend6791 gtfo
@@sherueatyourbestfriend6791 ofcrse🐒
@@sherueatyourbestfriend6791 stfu
Can you make a separate video on how you did adult calculus?
its on his main channel, epsilon delta definition.
Epsilon Delta 👍
God damn that was clean
Still I choose to be a baby
Real adults know that 3x-1 is a continuous function and just plug in x=2
Can we get the limiting value(not proof. Here you are proving from already known value 5) using epsilon-delta definition of limit?
The thing I don’t get about epsilon-delta proofs is the “choose” part, I can’t understand how I have to choose, is there a formula for the right answer or what?
Also the suppose part
Well if you were to choose another number it wouldn’t work, so you need to choose the one that does work
. 4@9. Pipe west favgot
Who's we 😟 cause I don't see
Nǐ hái yǒu shé me wǒ kěyǐ miǎnfèi xiàzài de
It feels like you have to get a phd to understand the epsilon delta definition
I always thought the same
In my experience of getting a minor in mathematics, epsilon delta proofs of limits only really comes into play later in the upper level classes. The first time I looked into them in detail was Real Analysis. This was after calcs 1-3, Linear algebra, and abstract algebra.
@@gregsavitt7176 could i ask the reason for formalising such concepts? I mean i know it's standard practice to have everything rigorously defined, but is That really necessary?
@@Qrudi234 To answer your question, yes it is, but not for exercices like this video and very rarely for computation purpose. I see 2 reasons. 1) It is necessery to have a proper limit definition in order to generalize limits to metric space as they are often not as intuitive and 2) at some point, results in analysis are not as trivial and need epsilon argument to properly prove them.Just to name a few, results tied with Cauchy sequence, uniforme convergence, compactness and completeness often need such argument (but not necessarily in more general topologycal context, but that's another story).
@@francoislaniel868 Okay, i already figured the first reason, being that it gives way to generalising the definition. Thank you for your time
I love how he switches the pens
Idk why but your profile pic somehow matches your comment
That's why he's called Black pen Red pen. 😉
@Frederick-111 i don’t think so, a simple compliment matches a non-set pfp
@@tamaz88 you had a troll dispair pfp when I made the comment that's why it was so funny to me
@@Frederick-111 well, I kinda see what you were thinking
The most amazing thing was switching of markers
Welcome to blackpenredpen
One of the things that suck to be an adult
we're literally at the point where we are learning limits
and please don't scare my classmates
bro I know how to get simple definite and indefinite integrals. by simple i mean something like no fractions or trigonometry in the equation but still while solving it it can have trig
I HATE THE EPSILON DELTA DEFINITION OF LIMITS
I HATE THE EPSILON DELTA DEFINITION OF LIMITS
I HATE THE EPSILON DELTA DEFINITION OF LIMITS
I HATE THE EPSILON DELTA DEFINITION OF LIMITS
I HATE THE EPSILON DELTA DEFINITION OF LIMITS
Hey guys, did you know that I hate the epsilon delta definition of limit
Yes we get the gist
🤣😂
Do you want to know the dark side, where you can just show that if x is infenitesimaly close to 2, then 3x-1 is infenitesimaly close to 5 and it will be formall proof?
Take d -any infenitesimal
f(2+d)=3(2+d)-1=5+3d≈5 qed
Facts
That adult calculus thing is way sadder than it looks
How did you know that you were going to choose |x-2|?
It comes from practice and noticing things carefully
He is not really choosing it to be that. For an epsilon-delta proof you need to show that for any given epsilon there exists a delta (both positive), such that the statement 0
x is approaching 2, so we need |x-2|, the distance between them, to be arbitrarily small.
U are basically proofing that 3x-1 is continuous in 2 that’s why we look at abs value of x-2
It follows from the definition
Even adultwr calculus: "given that all polynomials are continuous, we can inmediately substitute in 2 for x in 3x-1, to get the limit as 6-1=5 qed
I used to hate epsilon delta proofs. I love them now
I finally understand this. Delta is a function of epsilon such that an infinitesimal rectangle with epsilon and delta as the legs can contain all points a distance dr away from the point in question. If this rectangle exists than we say the limit exists. This usually fails if for some small length epsilon the delta length is cut short from some singularity that is contained in the small rectangle.
Well Jesus is right when he said to be like children 😂
Much too frantic, slow down, go back to your teaching roots that we all love.
Tbf, what you actually do is just do the adult way to prove continuity of an arbitrary polynomial and then do it the baby way haha
Mathematicians when they get bored.
Wtf did i just watch? It's confusing?
what is that inverted 3?
The first one counts as adult calculus IF you've proved, and can cite, the limit laws that justify it.
I would probably understand if you'd explained to me what the symbols mean. The calculation makes sense to me.
It's the formal definition of a limit.
In the first method, he just plugs in x=2, and evaluates the expression to find the limit as x approaches 2. For this example, it's just a simple linear function, and we have no discontinuities, so there's no need to do anything more than that to find the limit.
The second method formalizes the process, in what we exactly mean by "approach". Send x arbitrarily close to 2 without being 2 exactly. Does (3*x-1) continue to get closer to 3*2-1, as x approaches 2? That's what he's calculating.
They call it the epsilon-delta proof, because epsilon and delta (the Greek equivalents of e and d) are the traditional symbols that are used for this process.
The epsilon delta definition of the limit is a hell of a lot more intuitive if you first teach kids the definition of the limit of a sequence. That intuition is enough for the form of the epsilon-delta proofs to make sense, but in the war against number theory unfortunately sequences aren't taught in school.
Sequences were taught in calculus where I'm from, but they were after almost everything else which I agree makes no sense
Man i love being a baby
Still useless to use "calculus" to find limit of function that are continuous
Bhai tu kya insaan hai 😢
Kids do direct substitution, men do Epsilon-delta
great and easy showcase on how to find the right epsilons for your proofs.
Adult calculus: largely irrelevant and unnecessary for normal use, making the intuitive version more complicated and time consuming.
Ig that says something about being an adult lol
I can understand some of what he's doing, is he just trying to find the value of X by finding the primitive within the domain?
Gigachad using nonstandard analysis
take any z≈2, let's say 2+epsilon for some arbitrary epsilon - infenitesimal.
Then 3z-1=6+epsilon-1=5+epsilon≈5
Hence the limit is 5
In non-standard analysis equivalent definition of limit is:
lim_x -> c f(x)=g if and only if
x≈c => f(x)≈g
where a≈b means that b-a is infenitesimal
based nonstandard analysis
I mean the E-D definition of limits arent that hard you will get the answer anyway by just substituding the x value
why do these math shorts always overcomplicate things?! Lol
The peace |3x+6| = 3|x+3| don't understand well why it valid.
And here I am with limits to infinity and continuity and discontinuity in Basic Calculus thinking its too much 😭😭 (im only in 10th grade help)
Never seen such a „manly” way to integrate😂
I am baby calculus 😂😂 I solve limits like the first one because It's my first year to learn calculus
The first way is not rigorous enough. You first have to prove that polynomials are continuous everywhere.
Proof by look at the graph
@@wavez4224 i dont need to lift my pencil.
QED
Proof: Obvious
it's very easy to show x is continuous and then use limit laws to show all polynomials are continuous. anybody doing math at a higher level would just plug in x=2
as a baby, i really thought limits are just another form of functions
Imagine doing precise definition for cubic functions hahaha death
Adult Calculus=College level calculus.
Baby Calculus= High school level calculus or lower
why we got the gujarati letter ઠ in here (jk it know its uhhh theta? i forgo 💀)
I don’t understand they guessing part of the e value
Adult trig is baby trig but with radians.
Let's introduce polar graphs and form
What kinda parents teaches calculus to baby’s?!
I have one yet simple question: what?
it made sense, until i fucking read it
As a 6th grader I actually got the first one right
𝔸𝕀 ℂ𝕒𝕝𝕔𝕦𝕝𝕦𝕤
To solve the limit \(\lim_{{x \to 2}} (3x - 1) = 5\) with step-by-step explanations, let's follow these steps:
1. **Understand the expression inside the limit**:
The expression we are dealing with is \(3x - 1\).
2. **Substitute the value \(x = 2\) into the expression**:
Since we want to find the limit as \(x\) approaches 2, we substitute \(x = 2\) into the expression \(3x - 1\).
\[
3(2) - 1
\]
3. **Perform the arithmetic**:
Calculate the value of the expression after substitution.
\[
3 \cdot 2 - 1 = 6 - 1 = 5
\]
4. **State the limit**:
Since the expression \(3x - 1\) is a linear function (which is continuous everywhere), the limit as \(x\) approaches 2 is simply the value of the function at \(x = 2\).
Therefore,
\[
\lim_{{x \to 2}} (3x - 1) = 5
\]
Thus, the limit is \( \boxed{5} \).
What else do you have I can free load
well thats mental issue not adult calculus
mm yes exquisite
Decrease your speed am not a genius😢
It’s basic algebra guys trust me… it just looks complicated
Too fast for me to understand this.
limits are literally addition
baby calculus = ignore any Calculus terminology (Lim, etc) and have fun...
adult calculus = do the problem....
bro is multipening
You Have to prove it..
Teenage Calculus: check that the function is not to be able to be evaluated + not continuous near the target value before using the epsilon-delta definition
huailiulin
Teenage calc has epsilon delta? 😵💫
asian maths, huh
Babies are the best....
Guess I'm a baby
Very easy .
Asian calculus: proof that statement by definition of Geine
That's it ?
as a baby calculus, can confirm.
Is it me or his “ marker switching “ is very smooth
me predending to understamd👀
Me: I can’t wait to be a adult
After seeing this:… or not
Huh
Baby calculus here
so that's the infamous epsilon delta proof (of the fundamental theorem of calculus I presume)... I don't long for the day I have to learn that
Why you posted that short on VALENTINE'S DAY ON 14 FEBRUARY 2023 ???
😂😂😂😂😂
Please don’t put real analysis on my feed
200
just definition lol, this one become baby calculus when I started to learn f(x,y) limit QwQ
😭
It's true 😊
Adult calculus is from advanced mathematics proofs theory.
Honestly;y I wish epsilon delta proofs were taught in calc, I still don't really get how they work and I'm towards the end of my 2nd year as a math major.
If the first is baby calculus, and the second is adult calculus, what do we call harder proofs than this.
Calc 3 and Differential Equation RN, and I still hate doing anything to do with limits and the summation symbol. JUST LET ME DO INTEGRALS AND DERIVATIVES
The baby would have used the continuity of the function 3x-2.
Is that an 8 in chosen and at the bottom (final answer) is that a backward 3? Wtf is thag
The first one can be seen as an adult calculus if you consider hyperreal numbers.
I love that when we do this, we do not accomplish anything, just an empty feeling
I have nothing in my brain like I have never study calculus before but I did.
Show your work be like
But does it approach the value from both sides?