A Turing machine cannot accept a language.

A Turing Machine will either accept or reject a string or loop forever. We know it accepts the string because it will halt in an accepting state. It is said to reject a string, of it halts in a rejecting state.

A TM recognises a language, if it halts and accepts all strings in that language and no others.

A Turing machine decides a language if it halts and accepts on all strings in that language, and halts and rejects for any string not in that language.

A total Turing machine or a decider is a machine that always halts regardless of the input. If a TM decides a language, then it is decider by definition or a total Turing Machine.

Edit:

To answer some of the questions in the OPs comments:

• A language does not define a Turing Machine. The TM defines the language; this language is set of all inputs that the TM halts and accepts on.

• All finite languages are decidable which means that there is a corresponding Turing machine which is a decider

A Turing Machine cannot accept a language.

A Turing Machine will either accept or reject a string or loop forever. We know it accepts the string because it will halt in an accepting state. It is said to reject a string, if it halts in a rejecting state.

A TM recognises a language, if it halts and accepts all strings in that language and no others.

A TM decides a language, if it halts and accepts on all strings in that language, and halts and rejects for any string not in that language.

A total Turing machine or a decider is a machine that always halts regardless of the input. If a TM decides a language, then it is decider by definition or a total Turing Machine.

Edit:

To answer some of the questions in the OP's comments:

• A language does not define a Turing Machine. The TM defines the language; this language is set of all inputs that the TM halts and accepts on.

• All finite languages are decidable which means that there is a corresponding Turing machine which is a decider.

A Turing machine cannot accept a language.

A Turing Machine will either accept or reject a string. We know it accepts the string because it will halt in an accepting state. It is said to reject a string, of it halts in a rejecting state.

A TM recognises a language, if it halts and accepts all strings in that language

A Turing machine decides a language if it halts and accepts on all strings in that language, and halts and rejects for any string not in that language.

A total Turing machine or a decider is a machine that always halts regardless of the input. If a TM decides a language, then it is decider by definition or a total Turing Machine.

Edit:

To answer some of the questions in the OPs comments:

• A language does not define a Turing Machine. The TM defines the language; this language is set of all inputs that the TM halts and accepts on.

• All finite languages are decidable which means that there is a corresponding Turing machine which is a decider

A Turing machine cannot accept a language.

A Turing Machine will either accept or reject a string or loop forever. We know it accepts the string because it will halt in an accepting state. It is said to reject a string, of it halts in a rejecting state.

A TM recognises a language, if it halts and accepts all strings in that language and no others.

A Turing machine decides a language if it halts and accepts on all strings in that language, and halts and rejects for any string not in that language.

A total Turing machine or a decider is a machine that always halts regardless of the input. If a TM decides a language, then it is decider by definition or a total Turing Machine.

Edit:

To answer some of the questions in the OPs comments:

• A language does not define a Turing Machine. The TM defines the language; this language is set of all inputs that the TM halts and accepts on.

• All finite languages are decidable which means that there is a corresponding Turing machine which is a decider