I was sitting in advanced calculus yesterday and my teacher must have watched Patch Adams the day before because instead of "I'm going to make doctors out of you" we got the "I'm going to make math majors out of you" speech and I had to bite my lip to stop from laughing.

We were trying to prove that the sequence: an = (√n+1)/(n+7) converges to 0, which it does(take the limit as n ->∞ and you will get 0).

The proof goes as shown below:

Let ε > 0

Choose a positive integer N such that N > 4/ε^2

Then if n≥N we have

|an - A| = |(√n+1)/(n+7) -0|

= |(√n+1)/(n+7) |

= (√n+1)/(n+7)

≤ (√n+1)/n

≤ (√n+√n)/n

= (2√n)/n

= 2/√n

≤ = 2/√N

< 2/(2/ε)

= ε

therefore the sequence converges to 0.

After we got done with this proof one of the kids in the class raises his hand and asks if every step in the math portion of the proof had to be shown(as you can see thats a lot of work to show). The teacher didn't really get what he was asking so she said "Yes" and the student fought with her for about 5 minutes about not wanting to show all his work. After about 5 minutes of them arguing the teacher and about 5 students in the class(me included) just look at him and in unison say "Just do the work." And then the teacher goes on this rant on how any idiot can take derivatives and integrals but it takes a special person to be able to write down why they work the way they do. And what she was trying to do was teach us how to write like mathematicians to separate us from the evil engineers(sorry all those engineers out there). She ranted for about 10 minutes on this and it really felt like I was watching Patch Adams...lol. "I going to make math majors out of you". I left the class and busted out laughing in the hall.

We were trying to prove that the sequence: an = (√n+1)/(n+7) converges to 0, which it does(take the limit as n ->∞ and you will get 0).

The proof goes as shown below:

Let ε > 0

Choose a positive integer N such that N > 4/ε^2

Then if n≥N we have

|an - A| = |(√n+1)/(n+7) -0|

= |(√n+1)/(n+7) |

= (√n+1)/(n+7)

≤ (√n+1)/n

≤ (√n+√n)/n

= (2√n)/n

= 2/√n

≤ = 2/√N

< 2/(2/ε)

= ε

therefore the sequence converges to 0.

After we got done with this proof one of the kids in the class raises his hand and asks if every step in the math portion of the proof had to be shown(as you can see thats a lot of work to show). The teacher didn't really get what he was asking so she said "Yes" and the student fought with her for about 5 minutes about not wanting to show all his work. After about 5 minutes of them arguing the teacher and about 5 students in the class(me included) just look at him and in unison say "Just do the work." And then the teacher goes on this rant on how any idiot can take derivatives and integrals but it takes a special person to be able to write down why they work the way they do. And what she was trying to do was teach us how to write like mathematicians to separate us from the evil engineers(sorry all those engineers out there). She ranted for about 10 minutes on this and it really felt like I was watching Patch Adams...lol. "I going to make math majors out of you". I left the class and busted out laughing in the hall.