Promise not to fall: Not to x Don't

Por que na frase:
Promise Not To Fall
Usamos o NOT, ao invés de DON"T?
Desde já, agradeço!
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Avatar do usuário PPAULO 39795 6 32 695
The definition of DON´T is a command or entreaty not to do something (Webster´s Dictionary)
https://www.merriam-webster.com/dictionary/don't

As you are seeking guarantees here, not an order it´s signaled by "not to do", it´s less overbearing/demanding. It let´s open to the possibility of "not doing" (promise not fall - you may fall or not).
It´s a bit similar to "or not?" that leaves open to another possibility that is yes/yes sir!

https://dictionary.cambridge.org/grammar/british-grammar/questions-and-negative-sentences/not

https://www.easypacelearning.com/all-lessons/english-level-2/1341-promise-learning-how-to-make-and-promises-english-lesson

In this case, you can´t positively promise that you won´t fall/are not falling (anytime). Indeed, the person is asking you to "try not to fall". Again, there is another possibility open here, that of falling...