1) Band/Artist: The Limit
A soulful combination of doom, punk and heavy … Read Full Bio ↴1) Band/Artist: The Limit
A soulful combination of doom, punk and heavy rock, The Limit is capturing that mid-60s sound with a modern, heavy feel. The new super-group is delivering real-deal old school rock that is a downright blast. Featuring members of legendary punk OG's The Stooges, doom rock pioneers Pentagram, NYC Punk originators Testors, the guitar driven track brings back those foundational sounds that inspired generations of hard rock and metal artists.

Lineup:
Vocals - Bobby Liebling (Pentagram)
Guitar - Sonny Vincent (Testors)
Guitar - Hugo Conim (Dawnrider)
Bass - Jimmy Recca (The Stooges)
Drums - Joao Pedro (Dawnrider)

Album Title: Caveman Logic
Album Release Date: April 9, 2021

2) In the mid eighties, dutch producers Bernard Oattes en Rob Van Schaik released an album under the name “The Limit”. Hits included “Say Yeah”, “Crimes Of Passion” and “She’s So Devine”. After the album they went back to producing, with their biggest hit being “Love Take Over” by Five Star.

The Limit was a 1980s musical group composed of Dutch producers Bernard Oattes and Rob Van Schalk. They released a full-length album in 1984, which yielded the hit "Say Yeah". The song peaked at #17 on the UK Singles Chart and at #7 on the U.S. Billboard Dance/Club Play chart.

3) THE LIMIT : USA based power Rock Trio compared to Rush and Pearl Jam touring nationwide USA and Europe released “Reinventing the Sun,” Internationally 2008 on MCR.
Listen here: www.thelimitmusic.com

4) Minimal Electro/New Wave band act formed by Survival Records’s in-house photographer & cover designer on many of their releases, P. K Edgley. Only released 2 singles in 1981. Additional vocals by Drinking Electricity’s member Anne Marie Heighway.

-Singles:

o Shock Waves b/w Ok Go [1981] 7” Single; Survival (SUR 002)
o Take It b/w Do It [1981] 7” Single; Survival (SUR 004)

5) Hardcore/punk band from Palermo, Italy.

2009 - Smash It 7'' on Hanged Man Records

Real
The Limit Lyrics

Jump to: Overall Meaning ↴ Line by Line Meaning ↴

Tres de la mañana, pensando en ti, mi amor
No tengo troca nueva, pero te doy mi corazón
I love you, mi princesa, vamos a mirar
La luna, las estrellas y el mar
Te quiero conquistar

Te amo y esta es la verdad
Complementas mi alma

Y esa es la verdad, oh

Y así suenan, Los del Limit

Toma de mi mano, que te voy a llevar
A otro mundo donde existe la paz
Acerca tus lindos labios
Que yo te quiero enseñar
Todo lo que te amo te hablo con la verdad

Te amo, esa es la verdad

Complementas mi alma
Y esa es la verdad

Overall Meaning

The first verse of The Limit's song Real describes a scene taking place at three in the morning where the singer is thinking about their lover. The lack of material possessions is acknowledged, but it is replaced with the offer of the singer's heart. The rest of the verse is filled with expressions of love and a desire for the couple to watch the moon, stars, and sea together as the singer tries to conquer their lover's heart. The chorus repeats the phrase "Te amo" (I love you) and the idea that their love is the truth and the complement to the singer's soul.

The second verse builds on the first, as the singer invites their lover to take their hand and go to another world where peace exists. The singer wants to teach their lover everything they love about them and speaks more about the truth of their love. The chorus is once again repeated, this time with added emphasis on the idea that their love is the truth. The ending features the band's name being announced.

Overall, the lyrics of the song express a deep and sincere love felt by the singer towards their lover. They recognize the importance of their lover in their life and express a desire to share special moments together.

Line by Line Meaning

Tres de la mañana, pensando en ti, mi amor
At three in the morning, I'm thinking of you, my love.

No tengo troca nueva, pero te doy mi corazón
I don't have a new truck, but I'm willing to give you my heart.

I love you, mi princesa, vamos a mirar
I love you, my princess, let's go and look.

La luna, las estrellas y el mar
At the moon, the stars and the sea.

Te quiero conquistar
I want to conquer you.

Te amo y esta es la verdad
I love you, and that's the truth.

Complementas mi alma
You complete my soul.

Y esa es la verdad, oh
And that's the truth, oh.

Y así suenan, Los del Limit
And that's how Los del Limit sound.

Toma de mi mano, que te voy a llevar
Take my hand, and I'll take you.

A otro mundo donde existe la paz
To another world where peace exists.

Acerca tus lindos labios
Bring your beautiful lips closer.

Que yo te quiero enseñar
Because I want to teach you.

Todo lo que te amo te hablo con la verdad
All I love about you, I speak the truth.

Lyrics © BMG Rights Management
Written by: Ruben Leyva

Lyrics Licensed & Provided by LyricFind

To comment on or correct specific content, highlight it

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01Mountain3:15

02Don't Look Back4:32

PT3M43S

06Take me to the River3:36

07Wind She Told Me2:55

08Holding On2:41

09Tragedy2:15

10God Money3:04

11Approaching Zero2:55

12More Like You3:57

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Most interesting comment from YouTube:

Rogier Brussee

Here is an alternative definition of limit that is also rigorous. Call a function $k:[0,\infty] \to [0,\infty]$ a control function if it is non decreasing (ie. if $ \delta_1 \le \delta_2$ , then $k(\delta_1) \le k(\delta_2)$, and
$\inf_{\delta > 0} k(\delta) = 0$ (i.e. if $e \le k(\delta)$ for all $\delta > 0$ then $ e\le 0$.).

We say that $\lim_{x \to a} f(x) = L$ if for all $x \ne a$ in the domain of $f$, we have
$$
|f(x) - L| \le k(|x -a|)
$$
for some control function $k$.

Note that control functions may be infinite so this really is only a condition for $|x -a| << 1$.

Example: Prove $\lim_{x \to 0} \sin(x)/x = 1$.

Proof:
Recall that for all real (or complex) $x$, the sine function can be defined as
$$
\sin(x) = \sum_{n=0}^{\infty} (1/(2n + 1)!) x^{2n + 1}.
$$
Therefore for $ x \ne 0$ we have
$$
\sin(x)/x = 1 + \sum_{n=1}^\infty (1/(2n+1)!) x^{2n}.
$$

Now for $0 < |x| \le 1/2$ we have
$$
|\sin(x)/x - 1| = |\sum_{n=1}^\infty (1/(2n+1)!) x^2n|
\le \sum_{n=1}^\infty (1/(2n+1)!) |x|^{2n}
\le \sum_{n =1}^\infty |x^{2n}|
= |x|^2/(1 - |x|^2)
\le 2 |x|^2.
$$
Hence $k(\delta) = 2 \delta^2$ for $\delta < 1/2$, (and $k(\delta = \infty$ for $\delta > 1/2$) is a control function showing $\lim_{x \to 0} \sin(x)/x = 1$.

To make contact with the standard definition of limit in the video: using the above one sees that
for all $\epsilon > 0$, and for $\delta = \sqrt{\epsilon/\sqrt{2}}$,
we have
for all $x$ with $0<|x|< \delta$ that $|\sin(x)/x - 1| < \epsilon$.

To get a $\delta$ from an $\epsilon$ boils down to "inverting" the control function (it is not quite inverting because the control function need not be increasing, only non decreasing but one can simply take the largest delta in $k^{-1}(\epsilon)$) This always works

See
https://drive.google.com/file/d/13J5gwhIkPuaFi84li5DM0G6PmjpucS_q/view?usp=sharing

for why this is equivalent to the standard definition in the video, and how this allows to say that some limits converge fast and others converge only slowly.

All comments from YouTube:

Jaybee Penaflor

4y↑39

Ah, the wonderful memories of when I first encountered the formal definition of the limit have returned after watching this video!

Jaybee Penaflor

@Moncef Karim Aït Belkacem LOL 😂

Moncef Karim Aït Belkacem

2y↑1

Wonderful????

It broke my dreams, don’t show this to kids

Nicolás Ángel Damonte

4y↑30

It would be great if you could do some more challenging examples using the definition such as for sin x / x or complicated functions since no examples of those are usually available in books, always the same basic ones.

ENXJ

3y↑1

@bagula12 You're gay.

Nicolás Ángel Damonte

4y↑21

Thanks guys but I’m not saying I need to solve that limit, I’m merely suggesting it would be interesting (given the type of problems Michael solves) to include some more challenging examples. That’s all.

Λ

4y↑8

you can just use the squeeze theorem or abuse limit laws to deal with most troublesome functions. there is really no reason to give a drawn out ε-δ proof

bagula12

4y↑8

If you know have learnt the definition perfectly and understand it well then you should do the challenging proof yourself and if you cannot, eventually, then ask to other. But first you try yourself and I should say you can solve. When "you" we solve it yourself then the joy will be more for you! So try it yourself "first"!😁

Muwonge Evans Paul

3y↑5

I just love the humility you posses and the beautiful explanation u possess. U are a natural teacher. Thanks for your lovely lessons.

hokou

4y↑2

A very clear explanation, easy to understand for a beginner. Thanks for your sharing. It's a very nice video, especially for a freshman in maths.

azulpúrpura

4y↑6

Excelente video as always, if you can (and want) make more proof for a little bit complicated functions, that would be nice :3. Greetings from Mexico :), I can't afford a math collage so this is really nice u3u. Thanks again :)

yoav elbaz

4y↑3

in the last example you can also take delta to be equal to -4+sqrt(16+e) and you get(x-4)(x+4)isless than 16+e-16=e

Julia Pezant

Such clarity. Thank you so much for doing this for us.

Yorange

Thank you so much, explained better than anyone else I’ve watched cover this topic

Robert Telarket

4y↑2

The delta-epsilon definition for the limit is the most important concept and event in the history of the world bringing precision and rigor; brought forth by Bolzano, Cauchy and its final form by Weierstrass.

karolak kolo

@Robert Telarket yes but saying that's the most significant thing out of all formalizations is quite the claim

Robert Telarket

@無Prior to the delta-epsilon definition the limit was used by faith not rigor that not only math was on shaky grounds but everything from physics and chemistry that relied on it was as well and the real results from the latter two that created the modern world. This is not to say that there would be guarantee that their theoretical creations implied that in fact is how the physical world works. Math just helps them produce various models and they choose if possible the one that best fits the observations. The specific developments you asked for are more than thousands that you can find and see in their discoveries for almost two centuries!

無

What further developments did it enable?

Unedited

4y↑1

My calc 1 professor introduced the formal definition with the idea of target shooting. Not sure why that’s stuck with me over 4 years later, but maybe it was repeating the definition over and over in my head about 700 times

Steven Scott

I love the lucidity of Professor Penn's videos.

ad2181

The limit definition needs to include a "for all" x qualifier.

Ezra Steinberg

3y↑1

Excellent starter examples!

Beatorīche

4y↑1

Minor question: Is it common in the US to practice ε-δ proofs using concrete examples? The analysis textbooks in my mother tongue start by directly proving limit properties from the definition, which makes these types of examples pretty trivial – for instance, for the second one, the claimed limit follows directly from the continuity of the identity function and the multiplicativity of limits. Obviously, both approaches are valid, and I'm not really sure which one I prefer – I just wanted to note this because I found it interesting and ask for the perspectives of other people. From a didactic standpoint, practicing with these types of specific examples might help acquaint students with estimations – which are obviously a very fundamental tool in analysis –, especially if the ε-δ definition of a limit is introduced early on in the course; however, analysis courses already feature a lot of those estimations early on, so it might be a good idea to move directly to proving theorems rather than getting hung up on calculations.

Beatorīche

@VeryEvilPettingZoo
Here's the thing, though: you'll see a lot of ε-δ proofs in an analysis course either way. Going through the proofs of limit properties, not to mention proofs of theorems about continuous functions and other things you'll encounter later on in an analysis course, should yield enough structural understanding of ε-δ proofs to write one yourself. Not to mention that a lot of textbooks will leave the occasional ε-δ proof as an exercise, which means you'll get even more practice – in addition to ε-δ proofs you'll encounter in other courses. And if the analysis course introduces limits of sequences before ε-δ limits (which, in my experience, most of them do), there's really not much to learn because they're essentially the same on a structural level.

It might be a different story with calculus courses (in my country, we don't have anything analogous to those – math majors generally take analysis as one of their first courses), but in analysis courses, I don't know if this type of practice is really useful.

Stephen Beck

It’s good practice to be able to use the original limit definition. Of course we quickly move on to bigger things.

xRiccardo

4y↑1

Both approaches are important.

Michael Bauer

3y↑1

This was 1st semester math, 3rd week real analysis I ... I'm like 99% sure around 99% of students at that point are not gonna type up their homework in LaTeX. :D

... I mean, I do - or I try to find the time. But this ain't my first rodeo. Even if you can write LaTeX well, writing well-formatted proofs with correctly justified multi-line steps - if possible in some proof calculus, or if you need to include some diagrams... that's really a lot more time-consuming than just writing it down by hand (/with pen on a tablet). Still - pays to learn to do it early.

PUP

4y↑5

Just learned this in Calculus class.

Rogier Brussee

NTV Online

Thank you!

Leo Dijkstra

4y↑1

I can’t watch these kind of proofs without constantly hearing Tom Lehrer singing that there is a delta for every episilon :D

Mango

I loved RA 1. It was such a great class

Robert Telarket

4y↑1

It's very important in this definition with the wording. You must say for each "small" positive epsilon there is a CORRESPONDING delta... NOT for every epsilon there is a delta...

Robert Telarket

3y↑1

@jm90: We'll leave it at that!
East is east and west is west and the twain shall never meet!

jm90

@Robert Telarket I see :-) Well, in today's 2021 mathematics, the words "all" and "each" are universally accepted as mathematical synonyms. The distinction is in the word order: "For each epsilon there exists a delta..." is different from "There exists a delta for each epsilon..." It is the second phrasing that you're referencing when you describe the misconception that there exists a common delta that applies to each epsilon simultaneously.

By the way, the articles "the" and "a" have accepted meanings, too: "the" means "only one," whereas "a" means "at least one." I agree that this is all very confusing for beginners, but this terminology is now completely standard among professional mathematicians.

Robert Telarket

@jm90: Yes I am objecting!
In 1968 as an undergraduate and junior taking the advanced calculus on an exam we had to use the delta-epsilon method. I used the word "all" in my response and was penalized 15 points from that question with a comment from my professor! I at that time 19 years of age luckily understood the concept that young but admitted I made a serious mistake. Since then I've known better!
We shouldn't go by the English or any other Ianguage imprecise use of all and each. Sorry I don't agree with you, they are different in math.
If we say for all epsilon there is a delta that could be construed by a beginning student that for all epsilon there is only a = one delta which is not correct!

jm90

@Robert Telarket You're objecting to the use of the word "all" as opposed to "each"? Mathematically, "all" and "each" are synonyms. Is your concern that "for all epsilon, there exists a delta...." sounds too much like the very different (incorrect) statement "there exists a delta for all epsilon...."? I mean, maybe, but it's the word order that really matters here. I suppose adding the word "corresponding" is psychologically helpful, though, sure.

Robert Telarket

@jm90: True small is meaningless.
Again the important point is that Mike and others use incorrectly the word for ALL epsilon there is a delta...This is vague and misleading. That is why you need to say for EACH epsilon chosen there is a CORRESPONDING delta....

1 More Replies...

Jon Curry

I'm so impressed by this sir. The amount of vids I've watched on this are too numerous to recall. This is by far the absolute best presentation I've ever seen on this subject You know your shit, that's for sure. Well done man!!!!

samir tripathy

very well explained…. 💯

luee lee

4y↑1

i needed this

Thiago Milanezi

👏👏👏👏👏

Zanderz McCluer

Where does the |x+4|<9 come from? I understand the 3<x<5, but where do you you get the |x+4|<9?

Ellen Ancowitz

@ZaTee thanks!

ZaTee

x is at most 5 thus |x+4| is at most 9 (we are only interested in the upper bound)

Khalil Alseragi

but we know that a numbers in the neighborhood of a number is endless .

KimJi imnida

4y↑1

how did it happen that absolute value of x+4 is less than 9? I am confused.

FrostDirt

3y↑2

@Em Ae See since
3 < x < 5, the maximum value of x is 5. Therefore, |x + 4| < 9.

Em Ae See

3y↑1

Yeah idk, -1<x-4<1, add 8 u get 7<x+4<9 and can be -9<x+4<9, which is |x+4|<9?? Idk lol

Logmao Jillian M.

I am same

ENXJ

I see what you did, but I don't feel the intuition behind it. Please tell us more of the "why" instead of the "what". :)

XaXuser

but here in your definition u forced f to be continous at a which is not always the case

J B

If we take the limit of a function like f(x)=1 then delta will be 0 for all values of x and epsilon.

J B

4y↑1

@VeryEvilPettingZoo ok it clicked. For the constant function delta can be arbitrarily small regardless of epsilon, but not actually be 0. Thanks 👍

Jesús Hernández

4y↑1

For epsilon < 0

The1RandomFool

3y↑5

Your shirt is inside-out!

That Should Work

4y↑2

I have a need to be handheld too much for this channel I think, yet anyway

無

I would mention that in my next date if I were you. Long moonlit walks on the beach, Italian food, and holding hands while watching Michael Penn videos.

עומרי טאבו

3y↑4

Am I the only one noticed that he wore his T shirt reversed after 8 min into the video?

עומרי טאבו

@無 Hello there🤣

無

3y↑1

שלום!

Mercy Kyalo

Nice one

Reem Ahmad

thanx

Jim Allyson Nevado

I think this is too late to be placed in this series

Stephen Beck

4y↑1

He already did a bunch of limit/convergent proofs with series which is more important as a foundation for analysis in general. Now he’s starting to prove the big theorems of calculus which rely on the existence of convergent sequences in the reals to be rigorous, and so he picks up calculus with function limits.

chance rowland

4y↑3

Hey Mr.Penn your shirt is inside out ...

Robert Telarket

4y↑2

Well what do expect from an outstanding absent-minded mathematician? He cares about the subject matter not worldly things.
You are very observant and for that reason you're probably a mathematician.

Nuclo

4y↑1

14:20

bagula12

4y↑5

Why this definition is so late uploaded?

bagula12

4y↑1

@Wasparoo Oh! Thank you very much for your comment! Now I got it ! Thanks again!

Wasparoo

4y↑2

Most analysis 1 textbooks go: real numbers -> sequences -> series -> topology of the real line -> functional limits (which is what this is) -> continuity -> differentiation -> maybe integrals. It’s likely this is just the order of the textbook he is using.

John Gabriel

It cannot be a "proof" of any kind if you already know the limit L.

You're simply stating an unremarkable property of convergence.

A much better video is this one:

https://youtu.be/K4eAyn-oK4M

Sam Tetruashvili

3y↑3

It is a proof that the limit is indeed L. Your knowledge (or lack thereof) does not determine whether something is a proof. A statement is proven when it is demonstrably derived from its assumptions along with axioms. You can say that proof is trivial, but unless you can demonstrate an invalid step in the proof you cannot claim it is not a proof.