The ASL manual alphabet contains a total of 36 signs, one for
each letter of the alphabet and one for each digit from 0 to 9. ASL
is used when there is no official "sign" for the word that the
person wants to convey, for example, their name.
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Proper names are usually spelled out in sign language. Google
"manual alphabet".
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To spell "Helen Keller" in American Sign Language, you would fingerspell the letters H-E-L-E-N K-E-L-L-E-R using the manual alphabet. Each letter is signed individually.
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Technically, there is no such thing as the American alphabet,
but the English language does use the Roman alphabet.