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In the event of the president's death during the term or resignation, the vice president becomes president, followed by the Speaker of the House.
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Disagreements between the two formed early divisions within the government regarding policies on economics. They became the foundation for political parties as Hamilton wanted to have high trade tariffs and a centralized bank (Bank of the United States) and Jefferson wanted to concentrate on what would be good for the common man (the policies of the Democrat-Republicans).