Volume 1 / Part 2 — *82. SELECTIONS FROM RELATIVE PRODUCTS.
Reading edition
*82. SELECTIONS FROM RELATIVE PRODUCTS.
Summary of *82.
The propositions contained in this number are not much used except in connection with the associative law for cardinal multiplication, but they have a certain intrinsic interest. We prove in this number that, with a suitable hypothesis, ( results from by multiplying each member by , i.e.
*82·272.
Also under a suitable hypothesis the domains of ( are the domains of , i.e.
*82·32.
In the applications of propositions of the present number in *85, and are replaced by and . By *62·26, ; thus we obtain relations between and .
*82·2.
Dem.
*82·21.
Dem.
*82·22.
Dem.
*82·221.
Dem.
*82·23.
Dem.
*82·231.
Dem.
*82·24.
Dem.
*82·241.
Dem.
*82·25.
*82·251.
*82·26.
*82·261.
*82·27.
*82·271.
*82·272.
Dem.
*82·28.
*82·29.
*82·291.
*82·3.
Dem.
*82·31.
Dem.
*82·32.
Dem.
*82·33.
Dem.
The following propositions (*82·4·41·411·42) are lemmas for *83·43, which is used in the proof of *114·5, in the theory of cardinal multiplication.
*82·4.
Dem.
*82·41.
Dem.
*82·411.
*82·42.
*82·43.
Dem.
*82·45.
Dem.
*82·5.
*82·51.
*82·52.
Dem.
*82·53.
Dem.