mutual

1. Origins, structure, and basic meaning

• Structure: 互 expresses a mutual relationship rather than only one side. The word 互い is read たがい.
• Basic usage: 互いの考え means each other's thoughts, and 互いに助ける means to help each other.

2. Common pitfalls and similar expressions

• Mutually and alternately
  • 相互, read そうご, expresses a reciprocal relationship between sides.
  • 交互, read こうご, means alternately or in turns; helping each other does not necessarily involve taking turns.
• The roles of の and に
  • In 互いの考え, の connects to the following noun; in 互いに助ける, the whole expression 互いに modifies the action with the meaning “each other.”
  • The two forms are not interchangeable regardless of what follows.