hˈɛns ˈɛvɹi kəntˈɪnjuːəs fˈʌŋkʃən tə ðə ɹˈiːəl lˈaɪn mˈʌst biː kˈɑːnstənt, ænd hˈɛns bˈaʊndᵻd, pɹˈuːvɪŋ ðæt ˈɛks ɪz ɐ sˈuːdoʊkˌɑːmpækt spˈeɪs.
Hence every continuous function to the real line must be constant, and hence bounded, proving that X is a pseudocompact space.