By Harvey Rogert Margolis

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**Extra resources for Spectra and the Steenrod algebra: modules over the Steenrod algebra and the stable homotopy category**

**Example text**

It is, therefore, also the same pattern found in Babylonian mathematics. G. RADFORD 24 The first sought-after quantity, which appears at the left of the first column of the table (that is, at the left of the first vertical line; see below), is equal to seven (which is an abbreviation of the whole expression «7 numbers»); the second number From that, the (found to the left of the second vertical line), is equal to eight scribe finds that the third number is 300 plus fifteen and that the fourth number is 600 plus thirty .

All these approaches are, in fact, so familiar that many of us tend to take them as being only different appearances of the same essence. with the likely exception of (1). I will however argue that this is riot the case. We start by characterising what the equation ‘is’ in cach case. In (1) it is a condition to be fulfilled. THE PRODUCTION OF MEANING FOR ALGEBRA 39 In (2) it is a scale-balance. In (3) it is the do-list of a function machine. In (4) it is a whole-part relationship. In (5) it is a relationship ivolving numbers (including K) , arithmetical operations and equality.

I am quite sure that everyone in the mathematics education community will agree that solving an equation such as ‘3K+10=100’ is algebra. If for no other reason than because one has to deal with an ‘unknown’ expressed in literal notation, and dealing with literal expressions of this kind is algebra, even if it is not the whole of the subject. How can the task of solving ‘3x+10=100’ be fulfilled’? Certainly in a number of different ways: (1) Try different numbers, until you (hopefully) get it right.