It helped me ,Thanks....Funny thing is ,people are commenting it's 2020, it's 2019 but still helpful, as if ,the concept invented in the 19th century will change in 21st century or 2020 ....Still , thanks
Love from kashmir to legendary mathematician, u explained it in great manner, most of the math teachers explain it in quite bizarre way, u should start again
I still make videos occasionally, though not as often as I used to. If you have a particular math problem or question, let me know and I may be able to answer it with a video.
What an interesting function! I have not looked at this function before, but if you go to www.desmos.com/calculator you can graph it for yourself. (They use the notation "floor(x)" instead of the [x] bracket notation I used.) Here's what I got: www.desmos.com/calculator/fwpjhu1joo
So, for the Greatest Integer, you want the number that is smaller than the original number? Does that mean for the Least Integer, it would be the opposite? (Edit): Thank you soooo much. This helped me out a lot. My math lesson was explaining it weird. Thank you!
Yes, or more specifically, the Least Integer Function (aka, the Ceiling Function) gives you the least integer greater than or equal to x. Check out en.wikipedia.org/wiki/Floor_and_ceiling_functions
Thank you so much. I'll forever be indebted to you for this. But quick (and maybe even enormously dumb) question: in what condition will the lines you've plotted be parallel to the Y-axis? Is that even possible? Or will that happen if we were to do f (y) = [y]?
What a great question! And one with a few different answers, or at least a few different things to explore. First off, any relation that has a graph with one or more lines or line segments that are parallel to the y-axis, is not a function. (Remember the vertical line test?) But if you don't care that a graph is not representing a function, your question could become even more interesting: When you say "in what condition," are you asking about some real-world situation that could produce a graph with vertical line segments? (I don't know the answer to that question, but I'd love to hear if you have some ideas.) If you don't care about real-world situations and are only interested in a mathematical relation that produces a graph with vertical line segments, I am not aware of any already existing relation like that, but you could certainly invent one. How could you describe a relationship between some numbers that would result in a graph with one or more vertical line segments?
@@misc6412 You're very welcome, and don't beat yourself up too much over misconceptions about functions and relations. The concept of a function is foundational to pretty much all of mathematics, but there's an awful lot packed into it and most students don't fully grasp much of the concept until they've worked with it for a few years. (I know I didn't.)
Thank you so much, i have exams and this helps a lot, I've been taking online classes and my teacher doesn't explain that well online so its been hard. U gave a Pretty simple and fast explanation thank you again!
Thanks for the kind words. I am now an instructional coach, so now I work more with other teachers than I do with students. I still occasionally make instructional videos, but not as often.
There are many functions for which a derivative does not exist, and this is one of them. Functions that have "breaks" or discontinuities do not have a derivative; or more specifically, they do not have a derivative at the point(s) of discontinuity. So the derivative of the step function at each of the break points does not exist; and the derivative at all other points (i.e., where the graph is flat) is zero.
Hi Mehek! Can you give me an example of what you mean by "the fractional part of the greatest integer"? Two of the examples I worked thru on the first board in the video are [7.35] and [-2.5], each of which has a decimal (or if you prefer, fractional) part. Are you asking me to provide more explanation of examples like these?
Question: In the text book f(x)= [[x+2]] is graphed at [[-1]], when x=0 and y=2 on the chart. I cannot for the life of me figure out why the translation is taking place on the graph to [[-1]] for x=0 when algebraically [[2]] is the charted solution. The chart makes sense, the graph does not. If it were a proper translation, x+2=0 would be x=(-2), so why the [[-1]]?
Never mind, stupid mistake was made. I forgot to translate to the value of Y on the graph. I was interpreting y=0 as x=0 value instead of y=2 as stated by f(x). It can be confusing when you are dealing with greatest integer values with algebraic functions inside the greatest integer bracket. Thinking about this a lot more did help me see the solution though.
Hi Joel! I'm not sure what textbook you're referring to, but I *think* you're asking about the graph of f(x) = [[x+2]]. Here's a graph of that function using the desmos.com online graphing calculator: www.desmos.com/calculator/n3z9tzvbil . This graph doesn't display open and closed circles, so it's difficult to tell exactly where the graph is when x is equal to an integer value, but f(-1)=1, f(0)=2, and f(1)=3.
Hi Simran! The least integer function is not used nearly as often as the greatest integer function. There are several videos you can find online that discuss the least integer function. Here's one that's short and pretty clear: ua-cam.com/video/mLbxSVc7Pwg/v-deo.html
Hi Ananya! Most of my understanding of functions came from math classes and math textbooks. I don't really recall the names of any particularly useful textbooks, thought the internet is full of useful videos and articles on functions. Khan Academy would probably be a good place to start.
I'm not really an expert in this area, but my understanding is that in traditional Euclidean geometry, a line is NOT considered parallel to itself, but in other situations, it can be. For example, according to the "Parallel" Wikipedia entry, in 1957 Emil Artin "adopted a definition of parallelism where two lines are parallel if they have all or none of their points in common." So depending on the situation, it might make sense to define a line as being parallel to itself; or, it might not.
Hi God! Not sure I understand the question. Did I use the phrase "going over" somewhere in the video? If you'll tell me where (i.e., how many minutes:seconds into the video), I'll try to clarify what I meant.
its 2020, and this still helps me during virtual learning and zoom calls!!
Thanks Claire, glad it's helpful!
It's 2024 . This video still helps poor students
Thank you, glad it helped!
The best and clear explanation on step function. This video is still great even after 8 years.
Thanks Zayed, glad it helped!
I could not have dreamed of a better idea for this concept in 2022. Thank you very much Sir.
You're welcome!
It’s 3a.m and I’ve lost hope understanding this lesson until I watched your video . Thank you
You're welcome! Glad it helped!
It helped me ,Thanks....Funny thing is ,people are commenting it's 2020, it's 2019 but still helpful,
as if ,the concept invented in the 19th century will change in 21st century or 2020 ....Still , thanks
Yes, I continue to be pleased and surprised by how many people still say this video is helpful for them.
Its 2021 still this is helpful my maths problems. Thank lot..you saved me
You're welcome! Glad it helped.
Thank you very much sir .
LOVE FROM TAMILNADU,INDIA.
You're welcome!
Love from kashmir to legendary mathematician, u explained it in great manner, most of the math teachers explain it in quite bizarre way, u should start again
Thanks zeeshan, glad it helped!
Its 2021 and it still helps for zoom class
Thanks Sriram, glad it was helpful!
It’s 2019 and this is still very helpful! Thank you for this! ❤️❤️
Thanks Lexie, glad it helped!
Haha Im learning this right now in honors algebra 2 and I’m so confused!!
Hi Gracie! If you'll leave a question about what's confusing you, I'll try to help.
thank you so much for this video, I sincerely appreciate it, I teach myself and I spent the last 3 hours trying to understand this concept.
My college prof goes yapping abt step of x and stuff. i couldn't understand until i met this guy
I've had my share of students accuse me of unnecessary yapping, so I can relate. Glad it helped!
It’s 2021 and its still helpful
Thanks Abhiram, glad it helped.
The video was AWESOME!
it helped me a lot:)
Thank u so much:)
You're welcome! Glad it helped!
Best video on step function
Thanks Vihaan!
Greatest Integer Function made easy. Thanks for the video ..........
Thanks! Glad it was helpful!
Tysm✨ very helpful
You're welcome, glad it helped!
thanks Lance!
You're welcome!
This helps a lot thank you. Blessings from India.
You're welcome!
DAMNNNN THIS VIDEO HELPS ME A LOT
Yay! So glad it helped!
It's 2019 and this is extremely helpful for my final exam💖💖
Thanks Aseel, glad it was helpful!
Thbk you so muchhh your explanation works for me, I am struggling to find one and I am thankful I came across to this
You're welcome, glad it helped!
your teaching skills is awesome...thanks for the video
You're welcome!
Wish you could still make videos even up today
I still make videos occasionally, though not as often as I used to. If you have a particular math problem or question, let me know and I may be able to answer it with a video.
Thank you teacher ❤❤❤
but what is the graph of x[x] and where its continuous
What an interesting function! I have not looked at this function before, but if you go to www.desmos.com/calculator you can graph it for yourself. (They use the notation "floor(x)" instead of the [x] bracket notation I used.) Here's what I got: www.desmos.com/calculator/fwpjhu1joo
Thank you Berlin (from money heist) for teaching this🙏🏻
(Haven't seen Money Heist, but will put it on my list.) You're welcome!
@@lancebledsoe Sorry sir, for being sarcastic😄... But i really thank you for teaching it.. Well you have a great sence of humor too😄👍
Thank you! Clearly taught.
You're welcome!
You are an angel, Thank you so much
You're welcome!
So, for the Greatest Integer, you want the number that is smaller than the original number? Does that mean for the Least Integer, it would be the opposite?
(Edit): Thank you soooo much. This helped me out a lot. My math lesson was explaining it weird. Thank you!
Yes, or more specifically, the Least Integer Function (aka, the Ceiling Function) gives you the least integer greater than or equal to x. Check out en.wikipedia.org/wiki/Floor_and_ceiling_functions
@@lancebledsoe Thank you so much!
@@sweetocean3458 You're welcome!
Thanks well explanation simple and clear
Glad it helped!
This video is really helping me for my test on sunday
I’m back again studying for my math تحسين lol, still very helpful!!
Rewatching again for my finals
excellent explanation
Thank you, glad it helped!
Thankyou sir very helpful.(2022)
Simplified with details.
You're welcome!
Thank you 🙏🏻 very much you are help me
You’re fanc from iraq 🇮🇶
🙆♀️🙆♀️
You're welcome!
You are a life saver--thank you!!!
Thanks Gracinha, glad it helped!
Whoever downvoted this video has bad karma coming their way. This video is fantastic and this man is a saint.
Thanks Shane! Not sure I qualify for sainthood, but I appreciate the sentiment.
Thank you so much. I'll forever be indebted to you for this. But quick (and maybe even enormously dumb) question: in what condition will the lines you've plotted be parallel to the Y-axis? Is that even possible? Or will that happen if we were to do f (y) = [y]?
What a great question! And one with a few different answers, or at least a few different things to explore. First off, any relation that has a graph with one or more lines or line segments that are parallel to the y-axis, is not a function. (Remember the vertical line test?) But if you don't care that a graph is not representing a function, your question could become even more interesting: When you say "in what condition," are you asking about some real-world situation that could produce a graph with vertical line segments? (I don't know the answer to that question, but I'd love to hear if you have some ideas.) If you don't care about real-world situations and are only interested in a mathematical relation that produces a graph with vertical line segments, I am not aware of any already existing relation like that, but you could certainly invent one. How could you describe a relationship between some numbers that would result in a graph with one or more vertical line segments?
@@misc6412 You're very welcome, and don't beat yourself up too much over misconceptions about functions and relations. The concept of a function is foundational to pretty much all of mathematics, but there's an awful lot packed into it and most students don't fully grasp much of the concept until they've worked with it for a few years. (I know I didn't.)
Thank you so much, i have exams and this helps a lot, I've been taking online classes and my teacher doesn't explain that well online so its been hard.
U gave a Pretty simple and fast explanation thank you again!
You're welcome! Glad it helped.
100th Comment
Never Knew Steve Jobs is a Brilliant Mathematics Teacher
Thanks : )
(We do kind of favor each other, don't we?)
@@lancebledsoe Yes, You do look a lot like Steve jobs
If I ever saw you in an apple event from far I will believe Steve is back from heaven 😅
:)
I am from India.... Thanks sir for this vdo...
You're welcome!
Thank you!
You're welcome! Glad it helped!
Its 2021 and its still helping!😂
Thanks Akshreeya, glad it's helping!
Thank you sir
You're welcome! Glad it was helpful.
Thanks yo, this really helped me out!!!
You're welcome!
great videos, helps me a lot
Thanks kendude, glad it was helpful.
Thanks... This video cleared all my doubt..☺☺
You're welcome, Abhi! Glad it helped!
please keep posting more of these🙄🙄
thank you sir🙏🙏🙏
You're welcome!
thank you so much sir ..your explaination were so great ..can i text you for some questions about the whole integral ..
Hi Simon! Yes, please text me any questions you have, I'll answer them if I can.
Thank you very much, Very clear explanation.
You're welcome, glad it helped!
Thank you so much , saved my life!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Another life saved by math! Glad it was helpful, Reatile.
Thanks.Finally, I got it.
You're welcome Dario, glad it helped!
thank you sir god bless you from iraq
You're welcome!
Oh I just subscribed your channel😉😊
Awesome, though I don't post very regularly any more since I'm no longer in the classroom.
why did u stop videos? It is excellent explanation on step functions hope u will continue videos.
Thanks for the kind words. I am now an instructional coach, so now I work more with other teachers than I do with students. I still occasionally make instructional videos, but not as often.
Great....
Thanks!
better than 2019 explaining... thx
You're welcome! Glad it helped.
I want its derivative
There are many functions for which a derivative does not exist, and this is one of them. Functions that have "breaks" or discontinuities do not have a derivative; or more specifically, they do not have a derivative at the point(s) of discontinuity. So the derivative of the step function at each of the break points does not exist; and the derivative at all other points (i.e., where the graph is flat) is zero.
@@lancebledsoe i know but i meant its right and left derivative
Hey, could you explain the fractional part of the greatest integer? Great vid btw.
Hi Mehek! Can you give me an example of what you mean by "the fractional part of the greatest integer"? Two of the examples I worked thru on the first board in the video are [7.35] and [-2.5], each of which has a decimal (or if you prefer, fractional) part. Are you asking me to provide more explanation of examples like these?
Thank you sir ,it was simple to understand 🙂
You're very welcome, glad it helped.
THANKYOU SIR
You're welcome!
omg thank you
You're welcome!
Question: In the text book f(x)= [[x+2]] is graphed at [[-1]], when x=0 and y=2 on the chart. I cannot for the life of me figure out why the translation is taking place on the graph to [[-1]] for x=0 when algebraically [[2]] is the charted solution. The chart makes sense, the graph does not. If it were a proper translation, x+2=0 would be x=(-2), so why the [[-1]]?
Never mind, stupid mistake was made. I forgot to translate to the value of Y on the graph. I was interpreting y=0 as x=0 value instead of y=2 as stated by f(x). It can be confusing when you are dealing with greatest integer values with algebraic functions inside the greatest integer bracket. Thinking about this a lot more did help me see the solution though.
Hi Joel! I'm not sure what textbook you're referring to, but I *think* you're asking about the graph of f(x) = [[x+2]]. Here's a graph of that function using the desmos.com online graphing calculator: www.desmos.com/calculator/n3z9tzvbil . This graph doesn't display open and closed circles, so it's difficult to tell exactly where the graph is when x is equal to an integer value, but f(-1)=1, f(0)=2, and f(1)=3.
what about with least integer function? How do I graph that, along with the x and y table?
Hi Simran! The least integer function is not used nearly as often as the greatest integer function. There are several videos you can find online that discuss the least integer function. Here's one that's short and pretty clear: ua-cam.com/video/mLbxSVc7Pwg/v-deo.html
Thanks a lot...
You're welcome!
The video was very helpful, thank you, :)
You're welcome! Glad it helped!
This really helped a lot thank u sir^^
You're welcome!
I wish you were my math teacher🙄
Thank you! (I wish more of my students told me that.)
Thanks alot ☺️
You're welcome!
What does it means by solid dot and empty dot?
The solid dot includes the number it is on, a empty dot excludes that number
Wow..thank you..finally i'm understand.
You're welcome!
Thank you so much for this
You're welcome! Glad it was helpful.
Where are you from
Hi Gedda! I'm in North Carolina, in the US.
Sir, Can you please name some books that'll allow me to explore functions in much detail?
Hi Ananya! Most of my understanding of functions came from math classes and math textbooks. I don't really recall the names of any particularly useful textbooks, thought the internet is full of useful videos and articles on functions. Khan Academy would probably be a good place to start.
@@lancebledsoe Thank you
u r a dude !!
awesome !
thanks !
You're welcome! Glad it helped!
Sir, Is a line parallel to itself?
I'm not really an expert in this area, but my understanding is that in traditional Euclidean geometry, a line is NOT considered parallel to itself, but in other situations, it can be. For example, according to the "Parallel" Wikipedia entry, in 1957 Emil Artin "adopted a definition of parallelism where two lines are parallel if they have all or none of their points in common." So depending on the situation, it might make sense to define a line as being parallel to itself; or, it might not.
@@lancebledsoe I got it, Thank you
can we choose any x value or does it have to be a specific x value?
Hi jasmine! The value you use inside the brackets can be any real number.
Tnx a 👐lot
You're welcome!
What does going over mean here?
Does it mean that we should not write a digit over the given integer?
Hi God! Not sure I understand the question. Did I use the phrase "going over" somewhere in the video? If you'll tell me where (i.e., how many minutes:seconds into the video), I'll try to clarify what I meant.
@@lancebledsoe 3:23…what does that mean? Does that mean that we must not write the digit preceding it?
can u give more questions
Hi Sree! I'm not sure exactly what you're asking. Are you looking for more practice problems that you can work on?
Thanks
You're welcome!
thank youu!!! 🥰😭😭
You're welcome!
معدللللل عاشت ايدك
Superbbb
Thankyouuuuu😍
You're welcome Lexy, glad it helped.
Thank u
You're welcome!
Omggg!! Thank you so much! But I have some questions
Ask away!
Thanks❤❤❤❤ help me
You're welcome!
wierd 7 blurred hand wrinting. except this the whole was interesting and easier to learn
Thanks Mohammad, glad it was helpful.
Super
Thanks Gedda, glad it helped!
i love u
Math doesn't often generate such intense emotions, so thanks!
Mast
Thanks, praveen!
I don't know graphing function
Hi Noor, I'm not sure what you mean, but if you post a question I'll try to help.
Thank you sir.
You're welcome!