How many subsets in a set? (1 of 2: Induction proof)

[codystene]

I know I am a year late to this video, but Mr. Eddie Woo, if you ever see this, I just want to say thank you so so much, this definitely clarified this proof for me.

[jesusthroughmary]

The hint gave away everything. As soon as I read it my first thought was, "Oh, therefore adding an element doubles the number of subsets. All the existing subsets, plus each of them with the new element appended." So elegant.

[John_]

BTW binary arithmetic can be used to list all the subsets of a set. 0 means an element is not included in the subset, 1 means it is. Then count in binary eg 000, 001, 010, 011, 100, 101, 110, 111. Adding another element adds another binary digit which can be 0 or 1, thus doubling the number of subsets.

[RahnyT]

Hello Mr Woo, I was just wondering if it was possible to answer this question using a combinatorial argument? Because I noticed that if you had n elements, then you could choose n elements, or n-1 elements, or n-3 elements, etc, each with a unique amount of subsets. Meaning that, for the mathematical induction, you could prove nC0 + nC1 + nC2 + ... + nCn = 2^n

[AdamLaMore]

When introducing sets and subsets as a concept, you could have also related it to combinatorics since you had just refreshed that topic recently. Number of subsets in an n-set == sum of (n choose k) over range (0<=k<=n) == sum of the n'th row (zero-based) of Pascal's triangle.

[c.d.premkumar]

What is the reason for taking the number 2 as BASE in all these examples ? Like 2^2, 2^3, 2^4 etc.

[romanahmed]

hi, i m from Bangladesh. 1 question this topic- why every power set contain empty set??

[neetugoyal]

Sir please make a vedio of square and squares root

[syuliya]

lol.... so if one never seen a1, a2, / forgetting that resolution.... this is fantastic deductions at home, with fully understanding a question, and not letting pressure get to one.... and completely unique solution.... anyways it's awsome wish I saw something like this.... when I was in high school, would have aced fundamental math...

[aashsyed]

6:55 that really looks like a doughnut(torus in topology)

[ryang]

A small but pertinent correction: "the subsets i̶n̶c̶l̶u̶d̶e̶ _comprise_ subsets without l and with l"

[MichaelPiz]

What software are you using here? I could use it myself.

Thanks.

[neetugoyal]

Sir can you teach class 8 also in. Our area there is no best teacher I love study but I Found you so please start the class 8 It will really helpful for us students

[aashsyed]

he writes so beutifully is a good cool pro explainer

[lgl_noname]

17:31
*OBJECTION!*
Eddie, you just removed {} from the subsets for l=k+1

[aashsyed]

hey eddie! please read this comment! i want you to make some video on geometry! please!

[deathnote]

Sir how can someone like me who is really bad at math and hate mathematics can Learn and understand Mathematics easily ???