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"FARTHER" and "FURTHER"
"Farther" refers to physical distance. "Further" relates to metaphorical or non-physical distance. Ex.: The park is farther than I thought. We need to look further into this issue.
"IMPLY" and "INFER"
"Imply" means to suggest indirectly. "Infer" means to deduce or conclude from evidence. Ex.: Her silence seemed to imply disapproval. From her reaction, we can infer that she is unhappy.