2k+2 does not become 2k*2. The assumption is that 2^(k+1)>2k We have to prove 2^(k+1)>2(k+1)=2k+2 but we can sub 2k by our assumption in 2*2^k wich becomes 2*2k which is 4k or 2k + 2k
@@louisphilippe1100 Thanks I think I got it 2^k > 2k 2^(k+1)>2(k+1) we can exoand it and 2^k • 2 > 2k + 2 now we assumed that 2^k > 2k (why exactly do we sub a smaller number back in?)
Hey, I just failed my quiz on mathematical induction, thought it was easy, like you know plug and chuck. However, prof threw inequalities questions like this and I completely stopped thinking and mind went blanked. This vid explains too well, appreciated.
I just looked at some older examples of our exams, and saw these types of inductions and thought, oh well I better learn this now or it's gonna come as a question and I'll lose out on points.
At 2:53 is very confusing l when changing the equal sign.I got it.It make sense to make a new inequality from the first sentence by normal inequality rule
+Pariston Hill because 2^k is greater than 2k according to the assumption (step 2) therefore replace the 2^k in your initial expression with 2k to obtain a new expression which is definitely smaller, 2^(k+1) is identical to 2^k * 2 (expression 1) since you assumed that 2^k > 2k in your assumption stage, now replace 2^k with 2k to get, expression 1 > expression 2 (which is below) 2(k) * 2 (expression 2) therefore, 2^k * 2 > 2k * 2
Finally got induction with inequalities Don't noe if it's cause of your explaining or me just pouring over hundreds of videos and texts until it now finally clicked. Either way Dankii.
@@ziizoo_oo3995 It came from the assumption/ hypothesis part, remember that 2^k>2k, so we replace the 2k where there's 2^k in the proving part, hence 2^k*2 = 2k*2, 2k*2=4k = 2k + 2k.. Yeah? Hope it makes sense
How did 2k+2 become 2k*2??
EXACLTY!
I got it, thanks
2k+2 does not become 2k*2.
The assumption is that 2^(k+1)>2k
We have to prove 2^(k+1)>2(k+1)=2k+2
but we can sub 2k by our assumption in 2*2^k wich becomes 2*2k which is 4k or 2k + 2k
we talk about left hand side it is 2^(n+1) become 2^n*2
@@louisphilippe1100
Thanks I think I got it
2^k > 2k
2^(k+1)>2(k+1)
we can exoand it and
2^k • 2 > 2k + 2
now we assumed that 2^k > 2k
(why exactly do we sub a smaller number back in?)
Hey, I just failed my quiz on mathematical induction, thought it was easy, like you know plug and chuck. However, prof threw inequalities questions like this and I completely stopped thinking and mind went blanked. This vid explains too well, appreciated.
I just looked at some older examples of our exams, and saw these types of inductions and thought, oh well I better learn this now or it's gonna come as a question and I'll lose out on points.
At 2:53 is very confusing l when changing the equal sign.I got it.It make sense to make a new inequality from the first sentence by normal inequality rule
You are out of your mind, Teacher. You are not clearly explaining, sorry.
Where did the 2k . 2 come from?
man i think i understood it. i mean 2^1 times 2^k = 2k +2k. like 2^1 times 2 = 2 + 2 = 4 hhahahahaha i'm laughing right now like hell
Hey man thanks so much I had a hard time make much more sense when you can pause the vid rewind and rewind until you get it!thanks again!!
yeah there are some tricky steps it's hard to understand:)
i think youve messed up the exponent part because k became a variable multiplied to 2 rather than exponent of 2
thanks this was good for recapping on my knowledge
Awesome!!
very clean didn't confuse me when i wrote down and try it by myself !
Best explanation of inductions and inequalities, yet! Thanks so much :)
Daniel Castleman Hey thanks:) This is a tough one to learn for people!!!
Thank you so muchh!!! I have spec maths test tomorrow and i will try my best to use this knowledge !!
makes perfect sense! thanks man, I was struggling with this shit for hours.
Ny more videos based on this inequality by you ? thumb's up u made it real easy
This confused me more thanks
Wait how did it go from (2^k) * 2 into 2k *2? Did you accidentally turn exponent into a multiplier?
It was not accidental. Notice how he changed the equality as well.
he just did...because dude is a math sorcerer!
sry but how can you assume 2^k+1 is greater than 2k*2?
+Pariston Hill because 2^k is greater than 2k according to the assumption (step 2) therefore replace the 2^k in your initial expression with 2k to obtain a new expression which is definitely smaller,
2^(k+1) is identical to 2^k * 2 (expression 1)
since you assumed that 2^k > 2k in your assumption stage, now replace 2^k with 2k to get, expression 1 > expression 2 (which is below)
2(k) * 2 (expression 2)
therefore, 2^k * 2 > 2k * 2
+Abdullahi Osman oh ok -__- thanks!
Finally got induction with inequalities
Don't noe if it's cause of your explaining or me just pouring over hundreds of videos and texts until it now finally clicked.
Either way Dankii.
how did 2k+6 become 2k+2?
This is why people like him should be fired from teaching lmao
bro take a chill pill
Are you still active, sir?
yup!!!!!!
How did 2k+2 become 2k*2??
@@ziizoo_oo3995 It came from the assumption/ hypothesis part, remember that 2^k>2k, so we replace the 2k where there's 2^k in the proving part, hence 2^k*2 = 2k*2, 2k*2=4k = 2k + 2k.. Yeah? Hope it makes sense
Thank u
np:)
wtf is this
How did 2^K become 2k 🤣😂 .. some new math theory?
We assumed 2^k > 2k, hence in proving we replace the value of 2^k by 2k, not forgetting it is still >... Hence 2^k*2= 2k*2
@@mumbamulengajr.8358 it's 2^k*2>2k*2, not 2^k*2=2k*2
Thanks for wasting my time.