Truth is the correspondence between and one's beliefs about reality and reality. Though, truth itself is not necessarily limited to one's belief about something. For a statement/ideal/proposed fact to be considered "true," you must take it as it's definition. Truth doesn't imply that something has to be proven in order for it to be made true, but that the statement/ideal/proposed fact has to be true all of the time, regardless of one's belief.
Alfred Tarski defined truth in terms of an infinite family of sentences such as:
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