Hey guys, sorry for taking literally a year to respond to all of you :p To give you guys some background, I am currently a senior math and physics double major. This fall I will start my journey to get my PhD in Geophysics! I will try and post some new videos with proofs and possibly a few lectures. Discussions may include advanced topics like Finite Element Analysis as well as some simple but elegant proofs seen in Number Theory and in your Analyses courses. Let me know if you have any requests
@gooner4lifeJG It isn't: Try n=4. 5*6*7=210 which is not divisible by 12. You can however prove that (n+1)(n+2)(n+3) is divisible by 6 for all integral n.
Nice proof. Is it possible to give a general proof that NO PRIME NUMBER IS RATIONAL? It is simple to prove it for individual primes: 2, 3, 5, etc. Thanks.
Proof that sqrt(2) + sqrt(3) is irrational? Easy!
(sqrt(2) + sqrt(3))^2 = 2 + 2(sqrt(6)) + 3
= 5 + 2sqrt(6)
The square root of 6 is irrational, thus 5 + 2sqrt(6) is irrational, and since its square root is sqrt(2) + sqrt(3), we proved sqrt(2) + sqrt(3) is irrational.
@chach123123 By the Fundamental Theorem of Arithmetic, consider the unique representation of p=2^a 3^b 5^c ... for a,b,c non-negative integers. So, p^2=2^(2a) 3^(2b) 5^(2c)... Hence, if 3 divides p^2, then "b" cannot be zero. From our construction, it is clear that 3 divides p.
Hey guys, sorry for taking literally a year to respond to all of you :p To give you guys some background, I am currently a senior math and physics double major. This fall I will start my journey to get my PhD in Geophysics! I will try and post some new videos with proofs and possibly a few lectures. Discussions may include advanced topics like Finite Element Analysis as well as some simple but elegant proofs seen in Number Theory and in your Analyses courses. Let me know if you have any requests
djcoopdawg 2 months ago
how can i prove that
f(n) = (n+1)(n+2)(n+3) is divisible by 12 for all positive integral n
gooner4lifeJG 3 months ago
@gooner4lifeJG It isn't: Try n=4. 5*6*7=210 which is not divisible by 12. You can however prove that (n+1)(n+2)(n+3) is divisible by 6 for all integral n.
timelinesend 2 months ago
Do you tutor? I am taking a proof class and I have some questions.
MultiLiky 4 months ago
Nice proof. Is it possible to give a general proof that NO PRIME NUMBER IS RATIONAL? It is simple to prove it for individual primes: 2, 3, 5, etc. Thanks.
Rick
okzoia 7 months ago
Confused me by changing the letter s all the time
Why did this have to be done?
MrValzen 9 months ago
Proof that sqrt(2) + sqrt(3) is irrational? Easy!
(sqrt(2) + sqrt(3))^2 = 2 + 2(sqrt(6)) + 3
= 5 + 2sqrt(6)
The square root of 6 is irrational, thus 5 + 2sqrt(6) is irrational, and since its square root is sqrt(2) + sqrt(3), we proved sqrt(2) + sqrt(3) is irrational.
anticorncob6 1 year ago
what is the proof of the theorem that if 3 divides p^2 then 3 also divides p?
chach123123 1 year ago 5
@chach123123 By the Fundamental Theorem of Arithmetic, consider the unique representation of p=2^a 3^b 5^c ... for a,b,c non-negative integers. So, p^2=2^(2a) 3^(2b) 5^(2c)... Hence, if 3 divides p^2, then "b" cannot be zero. From our construction, it is clear that 3 divides p.
I hope that helps!
MattMiz03 1 year ago
thanks for this mate, really helped with a question i had
sayJUICE 2 years ago