Homeschool Math Blog

I've been doing math lessons with my 3-year old using the 100-bead abacus . Usually we do a few problems where she tells me a two-digit number to make, and I tell her a number to make, back and forth. Today she asked me to make 51, and I asked her to make 68. These went smoothly since she's getting pretty good at this now. Then we did a few "more than" problems. I said, "Let's say your sister has 5 cookies and you have one more than her . How many do you have?" This is a new concept to her, so we need to do it slowly and carefully with the abacus: first make her sister's cookies, then let her have the same amount, then give her one more. Then we did a few subtraction problems such as 7 − 4. She moved 7 beads, then "took away", or moved the other way, 4 beads. How many were left? 3 beads. I also showed her the subtraction 50 − 10 = 40. She started working on her own problem, "Let's do 9 − ..." and while she was thinki...

Recently this was highlighted at Slashdot and Digg.com both. A math professor James Anderson has made a new 'number' or entity that he calls NULLITY, in order to solve problems such as 0/0, which traditionally is left undefined. Basically he first defined 1/0 as infinity, -1/0 as negative infinity, and 0/0 as nullity, using Φ (Phi) as a symbol for it. He said this nullity lies outside our normal number line, not on it. I watched the video shown on BBC news , and there he went on to show what happens with the "age-old" problem of 0 0 , (zero to zeroth power) using just normal rules of arithmetic plus these definitions: 0 0 = 0 (1 − 1) = 0 1 × 0 -1 =(0/1) 1 × (0/1) -1 Now, for every number, the 1st power is the number itself, while the -1 power is its reciprocal: = (0/1) × (1/0) = (0 × 1) / (1 × 0 ) = 0/0 = Nullity. Anderson said in the comments following the main article on BBC that two other professors have helped him develop axioms for this...