幼儿园至二年级Category Theory计划中
Doing and undoing
Actions that change things (turning a card, adding a block, walking two steps forward), the action of doing nothing, and actions that can or cannot be undone, explored through play without any special vocabulary.
math.cat.actions-and-undoing
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前置知识
没有前置要求——从这里开始吧！
你将学会
- Describe the effect of an action on an object, such as 'turn the arrow a quarter turn'.
- Find the action that undoes a given action, and notice actions that cannot be undone, such as cracking an egg.
- Recognise 'doing nothing' as an action that leaves everything as it was.
定义
- An action changes an object or a situation, possibly leaving it the same.
- One action undoes another if doing the first and then the second puts everything back as it was.
- Doing nothing is the action that leaves every object unchanged.
定理
- 'Take 3 steps forward' is undone by 'take 3 steps back'.
- Some actions, such as mixing two paints, cannot be undone.
- Doing nothing and then doing an action has the same effect as just doing the action.
常见误解
- Thinking every action can be undone.
- Believing that 'doing nothing' is not something we can talk about as an action.
- Thinking that an action is always undone by doing it again; this works for flipping a card but not for walking forward.
通向
可选发现
- Composition Much later, actions become functions, doing nothing becomes the identity function, and undoing becomes taking an inverse function.
- Groups Collections of actions that can be combined and that can all be undone are studied in group theory.
- ← Addition, subtraction and place value to 100