Noah Webster's New International Dictionary of the English Language

1. (a.) Not capable of erring; entirely exempt from liability to mistake; unerring; inerrable.

2. (a.) Not liable to fail, deceive, or disappoint; indubitable; sure; certain; as, infallible evidence; infallible success; an infallible remedy.

3. (a.) Incapable of error in defining doctrines touching faith or morals. See Infallibility.