(Mathematical Induction) - Proof a set with N elements has 2^N Subsets

Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship. Beyond this, images of white Jesus are not just blasphemous and criminal, white Jesus is from Satan ( the imposter.) Why? Let's look at what Satan does:
1) He is incredibly narcissistic and promotes himself shamelessly.
2) He misleads and confuses.
3) He pushes people away from Jesus Christ God, the Holy Trinity, the one and only messiah. White Jesus does all three of the above and more -- matching the ways of Satan.

Statues of Christ are equally offensive to God the Christ. While money is the biggest idol, Jesus spoke sufficiently against carved images.
--------------------------------------------------------------------------------------------------------------------------------------------------------------

You can also find me on Tik Tok @reuslovesmath and @polarpiny

In this video, I show you how to use induction to prove that a set with N elements has 2^N subsets. This is a really neat proof and if you leave out the null set, you can do a similar proof showing that a set with N elements has (2^N)-1 Subsets.

[batoulalsayyed]

i understand everything except when he puts 2^k+2^k+1-1=2^(k+1) ?

[Rutika]

Thank you so much for the detail explanation

[Rsingh]

3:02 see that portion above these words case k+1
There are subsets with k-1 elements and k elements you habe repated a1 in them twice. Can you please explain?

[sridurganelapati]

What about single ton set like {A1}, {A2}....{ak} these also not repeating just like empty set then why 2power k minus one

[kiraivanova]

still i didn't understand the logic of proving it unfortunately :(

[adamkinsey]

This is very low quality. Typos on the screen ruin the proof( a1 repeated multiple times), and the verbal explanation is "yeah, uh-huh, alright alright, okay okay, like, um, additionally, this guy, and so on, you get it, right?" This is not an "explanation" of the proof. When extemporaneous speech isn't your strength, it is best to prepare a script, and then read it.