hypertown@lemmy.world to Memes@lemmy.ml · edit-21 year agoA meme for math peoplelemmy.worldimagemessage-square86fedilinkarrow-up11.02K
arrow-up11.02KimageA meme for math peoplelemmy.worldhypertown@lemmy.world to Memes@lemmy.ml · edit-21 year agomessage-square86fedilink
minus-squareGigglyBobble@kbin.sociallinkfedilinkarrow-up2·edit-21 year ago2^0 isn’t multiplying by zero. Considering this law: 2^a / 2^b = 2^(a-b) it’s obvious why 2^0 = 1 If a=b you’re dividing by the same number resulting in 1. Unfortunately, I cannot explain/prove the first law though.
minus-squarezalgotext@sh.itjust.workslinkfedilinkarrow-up3·edit-21 year agoThe first rule is just simple division: (2x2x2x2) / (2x2) = (2/2) * (2/2) * 2 * 2= 1 * 1 * 2 * 2 = 2 * 2 = 4 Writing in terms of powers: (2^4) / (2^2) = (2^(4-2)) = (2^2) = 4 The two bottom 2’s “cancel out” (really they just divide into one another to make 1’s) two of the top 2’s and you’re left with two top twos.
2^0 isn’t multiplying by zero. Considering this law: 2^a / 2^b = 2^(a-b)
it’s obvious why 2^0 = 1
If a=b you’re dividing by the same number resulting in 1.
Unfortunately, I cannot explain/prove the first law though.
The first rule is just simple division:
(2x2x2x2) / (2x2) =
(2/2) * (2/2) * 2 * 2=
1 * 1 * 2 * 2 =
2 * 2 =
4
Writing in terms of powers:
(2^4) / (2^2) =
(2^(4-2)) =
(2^2) =
4
The two bottom 2’s “cancel out” (really they just divide into one another to make 1’s) two of the top 2’s and you’re left with two top twos.