Doing and undoing

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ستتعلّم

• 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.

تعريف

• 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.

مبرهنة

• '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.

مفاهيم خاطئة شائعة

• 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.

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اكتشافات اختيارية

• 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