/sci/ - Science & Math

>>11382913
everything is hard

>>11382913
affirmative action

>>11382913
Did you try telling them that the point of the axiom of induction isn't to make proofs by induction possible, but to ensure the naturals are "small", which coincidentally allows for induction?

>>11382913
Probably because they are weak minded undergrads who don't fap to lolis 3 times a day, unlike us intellectuals.

>>11382913
If you are incapable of explaining something as simple as induction in such a way that even a single undergrad can see it clearly, your prospects as a quality teacher or professor really aren't looking good.

explain it like this

inductive step: if a domino falls, the the domino ahead of it also falls (for ever domino)

base case: the first domino falls

what is the result? all dominos fall

I was taught weak induction first, not knowing the difference between strong and weak induction and it set me up with bad habits. Some introductory Computer Science courses should be taught by Mathematicians.

>>11382913
Diversity acceptances

>>11382913
>Why is every single undergraduate I am teaching unable to grasp the concept

Because you SUCK as a teacher!!

>>11382913
You need to start with Peano's axioms.

If something is true for one element, it is also true for the next element
It is true for the first element
Therefore it is true for all the other elements

You don't need to bring in dominos or anything, it's very simple

>>11385888
G-d, I wish that were me except with a larger butt haha

>>11385966
So first step is IMPLICIT accept = induction

>>11382913
Try to use the dominos analogy. If you knock over the first domino and show that if a domino gets knocked over then the next in the sequence gets knocked over they all get knocked over. That'll allow them to understand it conceptually then you can abstract it and give a proper definition.

>>11383567
>to ensure that the naturals are "small"
Isn't it to ensure than there aren't any other sequences in the naturals like 1.5, 2.5, 3.5, ...? or that every natural should be reachable by repeated application of the successor function so to speak, since the other peano axioms alone should allow such a set to exist.

>>11386154
If you don't include the axiom of induction, you could have a set which is the union of the naturals and {x,y}, where S(x) = y and S(y)=x. This set satisfies all the other Peano axioms except induction.

>>11386587
Because it would be the inductive set itself so does not require further expansion.

>>11383567
I try to tell them the domino analogue but most zoomers have never played with dominos since they grew up with ipads

>>11386154
>Isn't it to ensure than there aren't any other sequences in the naturals like 1.5, 2.5, 3.5, ...?
That's what small means, even if that's a particularly well-behaved example.
>or that every natural should be reachable by repeated application of the successor function so to speak
That's basically the statement of the axiom.

>>11382916
not really.

>>11382913
The smartest student doesn't understand it.

The next smartest, hence, doesn't understand it either.

Therefore, none of them get it.

>>11387822
Was it supposed to be an explanation of induction?
If so, you're retarded.

>>11387834
No, it was meant to be a dumb joke. Dumb fucking piece of shit.

>>11382913

Have you tried using Illya as best girl as an example to teach them?

>>11382913
if none of them understand, it's probably your fault.

>>11387949
>Illya
>not kuro
you are never going to make it in the math world, kiddo