The Basic Sets - Where is 7?
ฝัง
- เผยแพร่เมื่อ 5 ม.ค. 2025
- In this episode of the Taylor Series, we build five of the most useful groups of numbers using only a few simple geometric shapes!
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Related Tidbits:
Set Builder Notation ( • I can't even )
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This is the first episode of the Taylor Series! Yay!
The Taylor Series aims to teach math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
I am aiming to have one new video up every month. I hope you enjoy them!
Also, I named this the Taylor Series after the mathematical construct created by James Gregory and formally introduced by Brook Taylor ... and I picked this one in particular because my name is Derrick Taylor. :)
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Patreon:
/ taylorseries
Facebook:
/ thetaylorseries
Twitter:
@TheTaylorSeries
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Music Credits (from AudioBlocks):
Intro music: Thinking by Patrick Smith
Main background music: Island Fun by Neil Cross
Outro music: Midnight City Lights by Neil Cross
How have people not discovered your channel? The quality is amazing
Same here, just found this channel
@@PatricioHondagneuRoig ikr, so underrated
Why didn't TH-cam recommend your videos to me? They are amazing, looking forward to watching more of your videos. Hopefully someday your channel will have an audience and people to teach them. Keep doing these well edited videos.
Thank god the youtube algorithm did something good for once *coff* "1 dollar condom vs 1000 dollar condom" *coff*
Video title: where is seven?
Man in video: I'm going to be talking about five different types of set
*mission failed, we'll get 'em next time.*
Hahaha. :)
Cool profile pic.
Zero is a natural number; change my mind.
Beautiful proposition.
Definitely when I got to college and grad school, I always included zero in the set of naturals, though this was largely for convenience.
Consider, though, the case of trying to invent the idea of numbers, but in a society that hasn't explicitly created them already. This isn't so far fetched; rewind the clock some thousands of years, and this is exactly the situation in which humans found themselves. Coming up with whole numbers is very natural, because you encounter whole numbers of objects all around you -- people, coconuts, whatever. Coming up with zero is actually not trivial. If what you're trying to do is describe what you literally see with your eyes, then zero feels useless; currently, right next to you, there are zero elephants, zero spaceships, so on (though if I'm wrong, you must then lead a more interesting life than me :) ). In fact, there's an infinite number of things next to you that we can count, and correctly enumerate them with a zero. In this way, zero feels paradoxical and kind of weird. Compounding the problem is the fact that language supplies a way of describing this situation already -- there are *no* elephants next to you. This doesn't feel like a number, so saying it can feel ... unnatural.
That isn't to say that we humans can't come up with zero -- in fact, we did, and found a lot of uses for it. And it's not to say that it spontaneously occur to someone in the civilization I proposed a moment ago. But, as a rule, there's an argument to suggest that encountering the idea of zero is not one that just sort of *happens* in the course of ones natural experience of the world, and so it's not unreasonable to say that it's not a natural number. And ultimately, that's the best I can do: suggest that it's reasonable not to consider zero a natural number. Utility, however, is king, and when it got right down to it, in my higher ed, we put zero in the set of naturals for convenience.
I am super glad you said this; I actually cut a part of the video that went over exactly this for time considerations. So, thank you. :)
But, we include zero in the set of whole numbers.
@@TheTaylorSeries I love this, thanks for sharing your knowledge and thoughts!
Zero defines an empty set. Null, nothing, insubstantial, lacking; no quantity, no place, not a number, but the absence of number.
YOU DONT NATURALLY START COUNTING AT 0
Who is the one person that disliked this? Why would anyone dislike this? It's just pleasant, well explained, and amazingly edited math.
I liked the video but maybe they disliked it because there was incorrect information
Your content is world class and needs more recognition
I love maths at a really high point, you explained this so nicely, complex/imaginary numbers always amazed me, but i don't understand them correctly, so probably your next video will help me)
Thanks for logically explaining my biggest problem in my last 5 years of school beatifully simple in 7 min
This guy makes math interesting, I subscribed!
Oh, there's the doorbell
Let's see who's out there
Oh, it's a seven
Hello, Seven
Won't you come in, Seven?
Make yourself at home
Hey, who's that other guy?
Is that your friend there?
"Oh, that's just Seven"
Another seven
Hello, Seven
Won't you come in as well?
Now who would like some cake?
("I would like some cake")
("Me too!")
What's that out the window?
A whole bunch of sevens
They're coming in now
And there's a lot of them
And down the chimney too
("Hey guys, come on in!")
I bet they want some cake
"We want cake! Where's our cake?"
My house is full of sevens
They're filling up the living room
Sliding down the banister
Talking on the telephone
Inviting over more sevens
("It's the green house at the end of the block")
I'm running out of cake
"We want cake! Where's our cake?"
My house is full of sevens
"We want cake! Where's our cake?"
Lots and lots of sevens
"We want cake! Where's our cake?"
Many more are stopping by
Sevens add and multiply
There's only one way to subtract them:
Let them eat up all the cake
I am afraid I missed the reference. But that's awesome to read at 5 in the morning. :)
The 7 apocalypse, 7 already 8 9, we should gather the weapons! Get ready!
From a they might be giants song for anyone wondering.
El Rocky O
Dude.
Everybody, even sevens, have to eat three squared meals a day.
@@TheTaylorSeries TMBG - Seven, Here Come the 123's th-cam.com/video/h9PNoJuP-mk/w-d-xo.html
I don't think the definition of algebraic numbers given at 5:00 is consistent with the roots of polynomials with integer coefficients definition because not all roots are solvable by radicals. Am I missing something?
Philipp Hoehn indeed, I was just about to write this. There are many numbers which - as he says, "cannot be written as a sum of roots" but are still algebraic. And even then, if we only consider those algebraic numbers that are roots of solvable polynomials, I'm pretty sure there's plenty of those that can't be "written as a finite sum of roots", too. I guess he was just trying to simplify the definition in a way which is more accessible to viewers who might not have any strong background in mathematics.
you're great at explaining and defining things well. I look forward to watching through your videos and keeping up in the future! [I also enjoy the dorky humor :) ]
subscribed. don't stop thr videos they are super interesting.
between 6 and 8
I’d say it is between 6.9 and 7.1 or 6.99 and 7.01 or 6.999 and 7.001 or 6.9999 and 7.0001. Im getting close, but never close enough
Seven is an unimaginable big number!
2:58 Woah, did I just get thrown back into music class?
Seriously though, maths and music (and surprisingly art) interlope quite a lot
Root of negativ one is not an algrebraic number , right?
I'll be honest, I've always disliked math. This was especially true back in school, where I struggled a lot, but you somehow make this so interesting! It takes some real talent to make entertaining content about a topic that some might dislike. Maybe something will finally stick. lol
4:40 ughhhh we have to memorize the first digits of the square root of 2, sqrt 2/ 2, sqrt 3, sqrt 3/ 2, and sqrt 3 /3 for precalc.
Let me guess: unit circle.
That just seems like bullyinh]g
I'm sure someone has built a wooden 7 for people to poke with sticks just to prove you wrong.
This would make me happy in ways words cannot encapsulate.
5:55 unless it's imperfect, 22/7=pi
but 22/7 = 22 ÷ 7 =/= pi. 22/7 is an approximation
His sultry clickbait gaze brought me here ❤
She's in Star Trek: Voyager.
She was actually a fraction.
@@TheTaylorSeries Don't you mean, "She was actually rational"?
In square enixs development hell
If this is your first video, why is the last in the playlist?
Even I followed along with this..
Set actually looks like the portuguese word sete, wich means seven, so this title sounds kinda funny to me😁
Oh nete! Er, neat. :)
It's in the title.
"Find x." "It's right there!"
@@TheTaylorSeries whats the f(-x)
f(-x)
𝕐𝔸𝕐!!
*Septebruary*
Right after Julvember.
Ohh yass primary school repeating.
Sets? Like what badgers live in? No, that's setts. A set of tables and chairs? A matching set? How can a quantity be in a set, if it already defines a set? A pair of pants, a trio, a myriad of ants.☆ If one were to say "sex" to a Swede, he would think of the number between five and seven. ...
Now please do the video in metric system for the rest of us non-American humans.
I actually find him misleading with this. One is gonna think that a triangle will have a hypotenuse of root 2 when the sides are 0.3048m in length which is wrong.
@@brzydka_i_bestia Regardless of units the answer is correct: length of 1 unit (foot) results in root 2 (same unit, feet) is correct. Imperial system is kinda sucky, I agree - but this also shows that the answer is univerally correct, regardless of units. Lengths one always results in root 2, but of course you already knew this. But then again metric system is much better IMHO.
7 ate 9
Gotta have three squared meals a day.
Or more precisely. Why is 6 afraid of 7? Because 7 ate 9.
5:58 I'd be more careful with your notation here. You're implying that even an infinite amount of terms isn't enough to equal pi, but this simply isn't true. The Leibniz formula is a counterexample to this. Modified a little to get the point across more, π = 4 - 4/3 + 4/5 - 4/7 + 4/9 - ... An infinite number of rationals can add to pi.
You're right, there is an infinite amount of terms that add up to pi. I didn't verbalize this, but that's why I put (finite) in parenthesis. :)
BUT. WHERE. IS. SEVEN.
IT'S RIGHT BEHIND YOU WATCH OUT AAAAHHHH
You basically just zoomed through people's ways of thinking and processing things from like the 4000+BC to nowadays
7 dislikes. How appropriate
Where is 7?
Halfway between 6 and 8 duh.
Eating 9
It's good to have three squared meals a day, after all.
Vsauce 2.0
You can't land on 3/8ths man! 7, however... well no. I don't think you can land on 7. In a way aren't they all imaginary?
Indeed! Now hopefully we can build rules that make them both useful and internally consistent. This won't help Dennis Hopper land on 7, tho. Sorry Dennis.
I think you can land on 3/8ths (etc.) because the ruler's marks have nonzero thickness.
The video is 7 mins
U poor guy having to mesure things with inches. I hope one day the us will be able to recognize the superiority of the metric system and adopt it so u will never have to use this outdated bad system again!
I know that this video is fairly odd but:
"Z stands for the german word Zahlen".
Again. There are dozens of examples of how german words are used in english but pronounced wrong. Why do scientists use german words, if nobody can pronounce them? Example: Schwarzschildradius.
And it is not only in science. "Zuckerberg" form Mark Zuckerberg definitly is german. It is not and english *and* german word like kindergarten. In english there is no "Zucker" or "Berg" it is in german. So why people pronounce it in english? I wonder how often other languages are used in english and are pronounced wrong. I'm sorry. I know that this is not necessary, but it annoys me everytime.
This happens in English with words taken from any language. An English speaker sees (or hears) a word of foreign origin and will pronounce it in a way that is more natural to them. But this doesn't happen only in English. Every language pronounces foreign words with a native flavor. I am learning Thai right now, and one word that comes to mind is "carrot." The word is the same in Thai... Except not quite. Thais say it more like, "car-LOT." The R sounds a bit L-ish, and the stress is on the second syllable.
So you've noticed something that happens naturally around the world, in basically every language. Annoyance is understandable if you know how the word "should" be pronounced. But you can also embrace it as the way language works, and how flexible language can be.
German contains sounds which do not exist in English, so when you say a word of German origin in English, you have to change the pronunciation to only use English sounds. You could have used better examples, however, since both "Schwarzchild" and "Zuckerberg" are names, so you can't make new words for them. Thus, you have to change the pronunciation to work in English.
On your second point, when English borrows words from a foreign language, for example, the word "dachshund", it would be difficult for English speakers to say it like it is said in German, because like I said before it contains sounds which do not exist or are uncommon in English. So "dachshund" is pronounced "Docks-hound" in English. It is not pronouncing it wrong like you said, it's just changing the word so it can be said in English. Would you prefer we ignore the German origin and just call it a "badger-dog"?