George Washington
At the end of his second term, Washington retired for personal and political reasons, fatigued and disgusted with personal attacks, and to assure a truly contested presidential election could be held. He did not feel bound to a two-term limit, but his retirement ultimately set precedent. The two-term limit to the presidency was formalized with the 1951 adoption of the Twenty-second Amendment to the United States Constitution. Washington is often credited with setting the principal of a two-term presidency, but it was Thomas Jefferson who first refused to run for a third term on political grounds.
President-elect of the United States
The president-elect assumes office as the next president of the United States upon the expiration of the term of the previous officeholder at noon on January 20. This procedure has been the subject of many misinterpretations and urban legends, such as the myth of David Rice Atchison's one-day-long presidency, which is predicated upon false assumptions and a logical flaw. Taking the formal oath of office does not affect the automatic accession to and occupation of the office of the presidency, which, in the case of the president, proceeds, ipso facto, from the expiration of the predecessor's term and the immediate start of the new four-year term. The oath of office is necessary so that the president can "enter upon the execution" of their office, but they are already president from the start of their term.