Terence Tao Solved Partially “Collatz Problem” (aka “3x+1“)

Terence Tao’s partial proof is inspired by similar problem pattern in PDE (Partial Differential Equation) : –

https://www.quantamagazine.org/mathematician-terence-tao-and-the-collatz-conjecture-20191211/

Changing Money 找钱数学

买物 $46, 我给售货员$50:
Buy goods at $46, I give the cashier $50 note, she changes money as follow:

英式 [UK Style Direct Subtraction] :找 $ 4 (50-46)
Mental calculation : Change $4 (50-46)

美国/法国式 [USA/French Style Add Back]补$4 凑 $50. Add $4 to make $50.

Another example: you bought something for $46.55, and paid with $50 note.

The cashier gives change by returning nickel (5 cents) and say $46.60, then 4 dimes (40 cents) and say $47, then $3 notes and say $50. Total Change is now $3.45.

中国式 [Chinese Style Round-Up Subtraction] :向你讨 多$1, 还整数 $ 5 (50+1-46=5)
Ask you to give 1 more $1, then change $5 note (50+1-46=50)

Conclusion:

UK style: Mental calculation 心算

French style : Reverse Calculation 逆算

Chinese style: “Abacus” Calculation 算盘

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