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It seems that all your definitions collude with the same single definition - "as a consequence / result of"

Let's see how this fits into each of your quoted verses:

  1. Don't eat chametz. As a result of that, you will remember...
  2. The result of someone saying "I will have peace" is that he will be satisfied (i.e. in this verse it is a not a result of not observing the mitzvoth, but a result of his saying that he will have peace, i.e., this is his thinking.)
  3. The first לְמַעַן seems superfluous because the same word appears at the end of the verse. Allow me some time to research this furtherSforno commentary fills in the blanks by in a sense, and I'll tryconnecting things to edit an answer if I locate onethe previous verse where G-d states that Avraham shal lbecome a great nation. Nonetheless.. (continuing in this verse, is the definition would still seem to mean "asreason why G-d is doing that) - "Because I know that as a result of"of (my making Avraham into a great nation), he will teach .... and as a result of his teaching his children....

    3A. The 2nd לְמַעַן means - As a result of teaching his children... G-d will bring unto Avraham what he has told him.

Yes, 3 and 3A, still seem a bit redundant even after explaining it this way, so, it still requires a bit more research...

It seems that all your definitions collude with the same single definition - "as a consequence / result of"

Let's see how this fits into each of your quoted verses:

  1. Don't eat chametz. As a result of that, you will remember...
  2. The result of someone saying "I will have peace" is that he will be satisfied (i.e. in this verse it is a not a result of not observing the mitzvoth, but a result of his saying that he will have peace, i.e., this is his thinking.)
  3. The first לְמַעַן seems superfluous because the same word appears at the end of the verse. Allow me some time to research this further, and I'll try to edit an answer if I locate one. Nonetheless, the definition would still seem to mean "as a result of".

    3A. The 2nd לְמַעַן means - As a result of teaching his children... G-d will bring unto Avraham what he has told him.

It seems that all your definitions collude with the same single definition - "as a consequence / result of"

Let's see how this fits into each of your quoted verses:

  1. Don't eat chametz. As a result of that, you will remember...
  2. The result of someone saying "I will have peace" is that he will be satisfied (i.e. in this verse it is a not a result of not observing the mitzvoth, but a result of his saying that he will have peace, i.e., this is his thinking.)
  3. The first לְמַעַן seems superfluous because the same word appears at the end of the verse. Sforno commentary fills in the blanks by in a sense, connecting things to the previous verse where G-d states that Avraham shal lbecome a great nation... (continuing in this verse, is the reason why G-d is doing that) - "Because I know that as a result of (my making Avraham into a great nation), he will teach .... and as a result of his teaching his children....

    3A. The 2nd לְמַעַן means - As a result of teaching his children... G-d will bring unto Avraham what he has told him.

Yes, 3 and 3A, still seem a bit redundant even after explaining it this way, so, it still requires a bit more research...

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It seems that all your definitions collude with the same single definition - "as a consequence / result of"

Let's see how this fits into each of your quoted verses:

  1. Don't eat chametz. As a result of that, you will remember...
  2. The result of someone saying "I will have peace" is that he will be satisfied (i.e. in this verse it is a not a result of not observing the mitzvoth, but a result of his saying that he will have peace, i.e., this is his thinking.)
  3. The first לְמַעַן seems superfluous because the same word appears at the end of the verse. Allow me some time to research this further, and I'll try to edit an answer if I locate one. Nonetheless, the definition would still seem to mean "as a result of".

    3A. The 2nd לְמַעַן means - As a result of teaching his children... G-d will bring unto Avraham what he has told him.