A DA-40 PILOT ON VISUAL APCH TO AN UNCONTROLLED AIRPORT HAD AN NMAC WITH A CESSNA DEPARTING IN THE OPPOSITE DIRECTION.

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ON DSCNT FROM THE S OF THE ARPT (FFC); I MONITORED AWOS AND NOTED THE WINDS WERE 210 DEGS/10 KTS; SLIGHTLY FAVORING RWY 13; SO I INITIALLY MENTALLY BEGAN SETTING UP FOR A R DOWNWIND ENTRY FOR RWY 13 (THE ARPT USES R-HAND PATTERNS FOR RWY 13). I THEN SAW AND HEARD ON THE CTAF FREQ AN ACFT ENTERING A L DOWNWIND FOR RWY 31. I REQUESTED THE RWY IN USE OVER CTAF AND SOMEONE RESPONDED THAT WINDS WERE BASICALLY ACROSS THE RWY AND THAT '31 WAS BEING USED AT FALCON FIELD TODAY.' SO; I CHANGED MY SET-UP TO A 45 DEG ENTRY TO A L DOWNWIND RWY 31. I ANNOUNCED AT THE 45 DEG POINT; ON THE DOWNWIND; TURNING BASE AND TURNING FINAL FOR RWY 31. I HEARD ANOTHER ACFT BROADCAST HIS TAXI-OUT -- I THOUGHT HE SAID 31; BUT IN 20/20 RETROSPECT; IT MAY BE THAT HE SAID 13. THEY SOUND SIMILAR OVER THE RADIO AND I WAS EXPECTING HIM TO TAKE OFF RWY 31 GIVEN MY CALLS AND THE ARR OF THE ACFT AHEAD OF ME JUST A MIN OR SO EARLIER ON RWY 31. AS I ARRIVED OVER THE THRESHOLD FOR LNDG RWY 31 I SAW ON OPPOSITE DIRECTION CESSNA COMING TOWARDS ME HAVING DEPARTED RWY 13 -- IF HE MADE A TKOF CALL I DID NOT HEAR IT. HE WAS ALREADY AIRBORNE AND HE TURNED R TO GET AWAY FROM THE RWY CTRLINE AND WAS CLBING WELL ABOVE ME AT THAT POINT. HE ANNOUNCED THAT HE WOULD BEAR R. I LANDED UNEVENTFULLY. I WAS MEETING A FRIEND (ALSO A PLT) AT THE ARPT AND HE SAW THE EVENT AND TOLD ME THAT THE WINDSOCK AT MY END OF THE RWY SHOWED I WAS LNDG INTO THE WIND. HE ALSO SAID THE OPPOSITE DIRECTION WAS INDICATED BY THE WINDSOCK AT THE OTHER END OF THE RWY. I BELIEVE A CONTRIBUTING CAUSE OF THE EVENT IS THE SIMILARITY IN THE SOUND OF THE NUMBERS 13 AND 31 WHEN HEARD OVER THE RADIO. I WILL EMPHASIZE THE PROPER PHRASEOLOGY IN THE FUTURE AND QUESTION OTHER PLTS WHEN THERE IS ANY POSSIBILITY OF CONFUSION; IE; DO NOT SAY THIRTEEN OR THIRTY ONE BUT RATHER ONE THREE OR THREE ONE; ALTHOUGH THAT COULD BE EASILY MISTAKEN AS WELL.