# "(I assume you mean the set of ordered pairs that contains only" #

# "the 1 pair given. If not -- please let me know !!!)" #

# "The question is:" \qquad \qquad "Is" \quad \ R \ = \ { (0, 0) \} \quad \ "a function "?" #

# "Here are two different reasons" \ R \ "is a function." #

# "1) If" \ \ R \ \ "were a not a function, it would contain a first" #

# "coordinate, say" \ a, "that is paired with more than one second" #

# "coordinate, say" \ b_1 \ "and" \ b_2 \, \ "where" \ b_1 != b_2.#

# "So then:" \qquad ( a ,b_1 ) \quad "and" \quad( a ,b_2 ) \quad \ "are two distinct points, and" #

# "they both belong to" \ R. #

# "But this is impossible --" \ R \ "contains only one point.
" #

# "So:" \qquad \qquad \qquad \qquad \ R \ = \ \ { (0, 0) \} \ \quad "must be a function." #

# "2) The only first coordinate" \ R \ \ "has, is" \ \ 0, \ "and it occurs only" #

# "once. So there are no repetitions in the first coordinates." #

# "Thus:" \qquad \qquad \qquad \qquad \qquad R \ = \ \ { (0, 0) \} \ quad "is a function." #