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By Fokkinga M.M.

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Extra resources for A gentle introduction to category theory. The calculational approach

Example text

When the fraction is transposed, the multiplication becomes a division and the division becomes a multiplication. It is because of this double change to the inverse that there seems to be no change at all. This can be made plainer by handling the fraction one piece at a time. Since ( e ) x signifies 2 2x multiplied by x divided by 5, it can be written -=-, 5 and the equation ( - J x = 18 becomes 46 ALGEBBA and then transpose the 2, so that Or, if you preferred, you could first transpose the 2 to give (or 45) Or perhaps you would like to work with decimals.

An expression like involves both a multiplication and a division since it stands for a multiplied by x and then the product divided by b. ) When the fraction is transposed, the multiplication becomes a division and the division becomes a multiplication. It is because of this double change to the inverse that there seems to be no change at all. This can be made plainer by handling the fraction one piece at a time. Since ( e ) x signifies 2 2x multiplied by x divided by 5, it can be written -=-, 5 and the equation ( - J x = 18 becomes 46 ALGEBBA and then transpose the 2, so that Or, if you preferred, you could first transpose the 2 to give (or 45) Or perhaps you would like to work with decimals.

In other words, can be written simply 4x and, in algebra, this is almost always done. It will be done from here on, in this book. In order to use this very convenient system even when only numerals are involved, parentheses can More Old Friends 37 be used. Each number involved in the multiplication is enclosed in a parenthesis showing that it is a number all by itself; thus, (4)(6) or (46)(23). The numbers are thus kept apart and cannot be 46 in the first place or 4623 in the second. Sometimes this is made more emphatic by using the multiplication dot and writing but this is not really necessary.

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A gentle introduction to category theory. The calculational approach by Fokkinga M.M.


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