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Numbers

Numbers. Counting manipulatives. Registers and addresses. EFT. Representations and algorism. Infinity is not a number. 1. 2. 3. 4. 1. 2. 3. 4. 5. Counting and addressing. “Have”. “At”. Counting distinguishable items. Register, bank account, address, and distance. 5. +5.

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Numbers

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  1. Numbers Counting manipulatives Registers and addresses EFT Representations and algorism Infinity is not a number 1 2 3 4 1 2 3 4 5

  2. Counting and addressing “Have” “At” Counting distinguishable items Register, bank account, address, and distance 5 +5 5 North +4 4 N 1 +3 3 N 4 +2 2 N 1 2 +1 1 N 3 0 Main street 1 2 3 -1 1 S 2 You are here -2 2 S 1 2 3 4 -3 3 S 1 $ -4 4 S -5 5 South 0 0 1 2 3 4 5 #

  3. Accounts without manipulatives “Have” “At” Counting distinguishable items Register, bank account, address, and distance 5 +5 5¢ 1 4 +4 4¢ +1¢ 1 2 3 +3 3¢ 1 2 3 2 +2 2¢ 1 2 3 4 1 2 3 4 1 +1 1¢ 0 0 0 0¢, empty 1 2 3 4 5 Bank account

  4. Accounts without manipulatives “Have” “At” Counting distinguishable items Register, bank account, address, and distance 5 +5 5¢ 5¢ 1 4 +4 4¢ 4¢ 1 2 3 +3 3¢ 3¢ 1 2 3 2 +2 2¢ 2¢ 1 2 3 4 1 +1 1¢ 1¢ 0 0 0 0¢, empty 0¢, empty 1 2 3 4 5 Account A Acct. B

  5. Quantum states without individually distinguishable particles “Have” “At” Counting distinguishable items Register, bank account, address, and distance 5 5 5 1 4 4 4 1 2 3 3 3 1 2 3 2 2 2 1 2 3 4 1 1 1 0 0 0 0 1 2 3 4 5 State B Quantum state A

  6. Preview: Bose-Einstein statistics “Have” “At” Counting distinguishable items Register, bank account, address, and distance ETOT,1 ETOT,2 5E1 5E1 E1 4E1 4E1 3E1 3E1 ETOT,0 5E0 2E1 2E1 4E0 3E0 E0 E1 E1 2E0 E0 1 2 3 4 5 0 0 0

  7. Preview: Bose-Einstein statistics “Have” “At” Counting distinguishable items Register, bank account, address, and distance ETOT,1 ETOT,2 5E1 5E1 E1 4E1 4E1 3E1 3E1 ETOT,0 5E0 2E1 2E1 4E0 3E0 E0 E1 E1 2E0 E0 1 2 3 4 5 0 0 0

  8. Preview: Bose-Einstein statistics “Have” “At” Counting distinguishable items Register, bank account, address, and distance ETOT,1 ETOT,2 5E1 5E1 E1 4E1 4E1 3E1 3E1 ETOT,0 5E0 2E1 2E1 4E0 3E0 E0 E1 E1 2E0 E0 1 2 3 4 5 0 0 0

  9. Preview: Bose-Einstein statistics “Have” “At” Counting distinguishable items Register, bank account, address, and distance ETOT,1 ETOT,2 5E1 5E1 E1 4E1 4E1 3E1 3E1 ETOT,0 5E0 2E1 2E1 4E0 3E0 E0 E1 E1 2E0 E0 1 2 3 4 5 0 0 0

  10. Preview: Bose-Einstein statistics “Have” “At” Counting distinguishable items Register, bank account, address, and distance ETOT,1 ETOT,2 5E1 5E1 E1 4E1 4E1 3E1 3E1 ETOT,0 5E0 2E1 2E1 4E0 3E0 E0 E1 E1 2E0 E0 1 2 3 4 5 0 0 0

  11. Preview: Bose-Einstein statistics “Have” “At” Counting distinguishable items Register, bank account, address, and distance ETOT,1 ETOT,2 5E1 5E1 E1 4E1 4E1 3E1 3E1 ETOT,0 5E0 2E1 2E1 4E0 3E0 E0 E1 E1 2E0 E0 1 2 3 4 5 0 0 0

  12. Number line “Have” “At” Counting distinguishable items Register, bank account, address, and distance 5 +5 5¢ 1 4 +4 4¢ 1 2 3 +3 3¢ 1 2 3 2 +2 2¢ 1 2 3 4 1 2 3 4 1 +1 1¢ 0 0 0 0¢, empty 1 2 3 4 5 Bank account

  13. Numbers Counting manipulatives Registers and addresses EFT Representations and algorism Infinity is not a number 1 2 3 4 1 2 3 4 5

  14. Notation Base representation and algorism Number line Wedge +5 10s +4 算盤, そろばん 9 +3 21041 8 +2 7 31051 + +1 6 5 0 4 -1 510 91 3 -2 2 -3 1 -4 1s 0 1 2 3 4 5 6 7 8 9 -5 #

  15. Numbers Counting manipulatives Registers and addresses EFT Representations and algorism Infinity is not a number 1 2 3 4 1 2 3 4 5

  16. Infinity (∞) is not a number +5 +4 ∞ is an instruction to “continue without bound or end.” +3 ∞ describes an ongoingprocessof moving along the number line ∞ does not identify any single location on the number line ∞ is not a number(at least for this course) +2 +1 0 lemniscate -1 -2 -3 -4 -5 #

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