https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:proofs-in-mathematics/x06d55bfa213a79fd:mathematical-statements/v/what-is-a-mathematical-statement 2026-03-11T06:20:45.557347727Z What is a mathematical statement? Mathematics becomes much more powerful when we understand how statements are formed and used in logical reasoning. This lesson explains what a mathematical statement is and how it differs from everyday sentences. Through clear definitions and simple examples, it shows how mathematicians decide whether a statement is true or false. The discussion also introduces how such statements form the foundation for proofs and logical arguments. A great starting point for students who want to think more clearly and confidently in mathematics. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw What is a mathematical statement? Mathematics becomes much more powerful when we understand how statements are formed and used in logical reasoning. This lesson explains what a mathematical statement is and how it differs from everyday sentences. Through clear definitions and simple examples, it shows how mathematicians decide whether a statement is true or false. The discussion also introduces how such statements form the foundation for proofs and logical arguments. A great starting point for students who want to think more clearly and confidently in mathematics. https://cdn.kastatic.org/ka-youtube-converted/vK1de1Iq0O4.mp4/vK1de1Iq0O4.mp4 693 Mathematical Statements https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:proofs-in-mathematics/x06d55bfa213a79fd:mathematical-statements/v/different-forms-of-theoretical-statements 2026-02-18T21:20:35.275198076Z Different forms of theoretical statements In this video, we dive into the world of theoretical statements—the backbone of mathematical reasoning. We begin by introducing what a mathematical statement is: a declarative sentence that is either true or false, such as “If a number is even, then it is divisible by 2.” From there, we explore how to negate a statement, flipping its truth value while preserving logical structure. Next, we unpack the converse of a statement—what happens when we reverse the hypothesis and conclusion—and discuss why the converse isn’t always true, even if the original statement is. Finally, we explore the powerful technique of proof by contradiction, where we assume the opposite of what we want to prove and show that this assumption leads to a logical inconsistency. Through intuitive examples and step-by-step reasoning, this video builds your understanding of how mathematicians construct and challenge ideas using formal logic. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction to theoretical statements 00:58 Negation of a statement 02:53 Converse of a statement 05:08 Proof by contradiction Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Different forms of theoretical statements In this video, we dive into the world of theoretical statements—the backbone of mathematical reasoning. We begin by introducing what a mathematical statement is: a declarative sentence that is either true or false, such as “If a number is even, then it is divisible by 2.” From there, we explore how to negate a statement, flipping its truth value while preserving logical structure. Next, we unpack the converse of a statement—what happens when we reverse the hypothesis and conclusion—and discuss why the converse isn’t always true, even if the original statement is. Finally, we explore the powerful technique of proof by contradiction, where we assume the opposite of what we want to prove and show that this assumption leads to a logical inconsistency. Through intuitive examples and step-by-step reasoning, this video builds your understanding of how mathematicians construct and challenge ideas using formal logic. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction to theoretical statements 00:58 Negation of a statement 02:53 Converse of a statement 05:08 Proof by contradiction Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy https://cdn.kastatic.org/ka-youtube-converted/iFtUgNM_zIg.mp4/iFtUgNM_zIg.mp4 362 Mathematical Statements https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:proofs-in-mathematics/x06d55bfa213a79fd:mathematical-statements/e/identifying-a-mathematical-statement 2026-02-20T04:00:32.356270105Z Identifying a mathematical statement In this exercise students will solve the problems on identifying whether given statements qualify as mathematical statements. Khan Academy exercise