Final answer:
Christopher Columbus believed that by sailing west, he would reach Asia due to a fundamental misunderstanding of the Earth's size. He made landfall in the Bahamas and Hispaniola, mistaking them for the East Indies, and continued to believe he was in Asia until his death.
Step-by-step explanation:
Columbus' claims about what he would reach by sailing west across the Atlantic were based on his misunderstanding of the size of the earth and the existence of the Americas. He expected to land in Asia, fueled by the misconception that the Earth was much smaller than it is.
Christopher Columbus set sail in August of 1492 and made landfall on an island in the Bahamas in October, which he mistakenly believed to be the East Indies. His voyages were continued under the belief that he was exploring parts of Asia and not a "New World".
Despite Spanish Exploration efforts elsewhere, such as Vasco da Gama reaching India, Columbus went to his grave believing he had reached Asia.
It was not until Ferdinand Magellan's fleet circumnavigated the globe that Columbus's errors and the true immensity of the Atlantic and the Pacific were confirmed. Ultimately, Columbus's voyages did open the way for the European exploration and colonization of the Americas, even though he never recognized the impact of his discovery at the time of his death.