# SFB 303 Discussion Paper No. A - 341

**Author**: Vind, Karl

**Title**: Figure 4 Lecture at Festkolloquium for Gérard Debreu

**Abstract**: This Festkolloquium for Gérard Debreu was organized somewhat informally. At one point it was suggested
that one speaker should talk about results related to the general (equilibrium) importance of
Gérard Debreu,
another about the unique importance, a third about the real importance, and even a forth about the marginal
importance. Finally it was of course decided that the speakers could choose their own subjects. I took up the idea
from the third suggestion. The title of my lecture could have been "What is the real importance of
G&eaute;rard
Debreu?" It could have been "Where did the real numbers come from?", but as mathematical economists we
should prefer answers to questions, and the answer to the two questions is "Figure 4".The "Figure 4" I am talking
about is Figure 4 in "Topological methods in cardinal utility theory" (1960). It obviously only requires
knowledge of the natural numbers to realize that Figure 4 could not be the only contribution of
Gérard Debreu,
but I hope to show that Figure 4 and its importance illustrates very neatly the real importance of
Gérard Debreu
for economics.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: July 1991

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