Thanks! Glad it was helpful

Thanks for the feedback and glad it helped!

😀

Same and learning online is shit too

do you know why he labeled x =5 as k?

You're welcome! Thanks for the positive feedback.

thanks! glad it helped.

You're welcome, glad it helped!

Nevermind, I figured it out. But, still confused about x= 5 is k.

Sorry I hadn't seen these comments earlier! This is just an exploration where it turns out that x = 5 gives us a nice C = 4 to make both sides equal. Then we can see that once x > 5, the inequality holds, so that makes the k = 5. After that, I show a much simpler way to do this. I tried to state that before this first example, but it seems some people missed that or got hung up on this example.

Is it because x^2 is the highest order in the function, and x = 5?

I believe he picked 5 as a arbitrary number to make it easier to pick c and k

have the same question, did u find the answer?

@@haneulkim4902 seriously wtf, this one thing has me so confused! the definition says x must be greater than k, but he set k to 5 when x was 5! i don't get it!

Ok lemme try to explain based on my knowledge. Let it be known that k is the "base case" of the possible values of input size n (the closest minimum value that satisfies the inequality). To perform what's on the left-hand side of the inequality (f(n)), we had to pick some value for n, which in this case is 5. We performed the left-hand expression and come up with the result of 100. Now we have to find a constant that would make the inequality true (i.e. to make 100

Sorry, I hadn't seen all of these comments earlier! The first example is just sort of done by exploration and it turned out that x = 5 gave us some nice numbers. The point is that once the functions become equal at x = 5, once we go beyond that (x > k, where k=5) we know the inequality will hold. I mention that later, there's a much simpler way to do this, but wanted to get the concept across first.

the whole strategy here is to find a C value to make the inequality hold. The easiest way to do that is to bump every term up to the highest degree and simply combine like terms. Then the C is right therw!

I appreciate the feedback. I tried to make it clear that this first example was done by exploration to illustrate the concept. The basic idea is that once x > k we need the inequality to hold. For this particular example, it was easy for me to find a value for k that gave us a nice C to make both sides equal. Once we get beyond this point where they are equal, the inequality holds. I stated that the following examples use a much easier strategy. Sure, maybe I should have added more examples for the exploration, but I am trying to keep the length of the videos down and focus on the strategy to find the C and k in the following examples. It seems like you were able to do that exploration on your own which is great!

@@discretemathvideos204 .... Appreciate the reply. Rest assure that it’s not limited to one youtube teaching channel. I’ve seen various youtubers doing the same regardless of subject matter. Often for beginners, tutorials having consistency makes a difference. Inconsistencies may cause confusion. Slow vs quick learners. Bart vs Lisa Simpsons of the world. Certain learners appreciate shorter videos, however, there are also a subset that prefer videos that are just a tad longer, with a couple more examples to truly hammer home concepts and the applications of those concept. Finding the right balance is certainly an art. I would rather see vids be a bit more thorough even if that adds one or two additional minutes - especially when they’re tutorials (as opposed to topic cliff notes). Specifically for ‘when x =5’ versus ‘when x > 5’, I decided to scroll through the comment section to see if someone may have offered clarification. Regardless, nice video. I got something out of it.

Sorry I hadn't seen these comments earlier! All you have to do is find a C and k for which the inequality holds. this technique does that in a quick and simple way. There is nothing incorrect in any of the statements.

Think about how that function you gave simplifies or use long division to simplify it.

That first example is really just done by exploration to explain the concept. I happened to notice that x=5 gave us a nice value for C. But the following examples show a much simpler strategy, so don't get hung up on where the 5 came from. It was just a value I knew would work well because I created the problem.

Sorry I hadn't seen these comments earlier! I'm not sure where you are referring to. But there is no unique k or C value, you just have to find a pair that works.

thanks for the explanation

the idea is that you are given the function f(x) and trying to say it is on the order of g(x). g(x) becomes a simple upper bound on f(x)

make a better one or get out buddy. this is the reason i have a degree.