Precedes

Now to derive Principle of Mathematical Induction from the General Principle of Induction, we formulate the instance of the latter in which a is 0 and R is Precedes:

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

That means we can define the successor function: n² = df the x such that Precedes (n, x)

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

To see an intuitive picture of why the Lemma on Successors gives us what we want, we may temporarily regard Precedes+ as the relation ‰¤.

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

(For the remainder of this subsection, the reader may wish to continue to think of Precedes+ in terms of ‰¤.)

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

Adm. Mullen's Call For Action Precedes Killing of 9 Soldiers ISLAMABAD, Pakistan -- Amid U.S. concerns about increasing insurgent activity in Afghanistan, the top U.S. military officer visited Pakistan's capital to press leaders here to crack down on militants destabilizing both countries.

U.S. Presses Pakistan to Check Militants 2008

- 11 Strategic Analysis • Starting point in the strategic management process • Precedes effective formulation and implementation of strategies

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