in one’s innermost feelings
心の奥で (kokoro no oku de)
"Deep down, she knew she was wrong."
"心の奥で、彼女は自分が間違っていると分かっていた。" (kokoro no oku de, kanojo wa jibun ga machigatte iru to wakatte ita)
to work hard and continuously
a person who refuses to believe without proof
something that will never happen
To spend less; to live frugally.
learning by experimenting and correcting mistakes
a discovery that changes understanding in a field