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An Introduction to Mathematical Reasoning by Peter J. Eccles

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1

The language of mathematics

Pure mathematics is concerned with the exploration of mathematical concepts arising initially from the study of space and number. In order to capture and communicate mathematical ideas we must make statements about mathematical objects and much mathematical activity can be described as the formulation of mathematical statements and then the determination of whether or not such statements are true or false. It is important to be clear about what constitutes it mathematical statement and this is considered in this first chapter. We begin with simple statements and then examine ways of building up more complicated statements.

1.1 Mathematical statements

It is quite difficult to give a precise formulation of what ...

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