Please type the answers to the following questions.1) a) Describe a “dialectic” style of debate. A dialectic style of debate is one where you argue against your opponent’s points rather than buttressing your own.b) Describe how Zeno would employ this style? (Make sure you use the work “paradox” your answer.Zeno would take his opponent’s arguments and try to prove logically that they were absurd.  They were called “paradoxes” since they would usually refute common beliefs.2) a) How did Zeno conclude “motion is impossible”?Zeno concluded that motion is impossible because to get from point A to point B, you would have to travel one half the remaining distance an infinite number of times, which is impossible.  Ergo, motion itself is impossible.b) Do you think he believed this conclusion? Explain. No.  Such a statement is so ludicrous that nobody could believe it.  There are also flaws in his logic, since 1/(infinity) would also equal 0, meaning it WOULD be possible to reach point B.3) a)If there was a race between Achilles and a tortoise, who would Zeno say would win? Explain. Zeno believes that the tortoise would win.  This is because when Achilles reaches the point where the tortoise moved forwards.  This repeats an infinite number of times, and Achilles is always behind.b) Describe the argument on pages 47-48 that show Zeno can be right and the Achilles will still win the race. (You can use words here instead of equations)Zeno is right, until a certain point.  His method of dividing the remaining time infinite times works until you reach that number.  If Achilles moves twice as fast, any point up to two seconds, Zeno is right.  At and beyond two seconds, Achilles is winning.  This is because the time in between each stop shrinks until it reaches 1/infinity, or zero.  c) on page 48 answer “Where did Zeno go wrong?” See 2b, his idea of “Achilles will not catch up because it will take infinite parts of time to catch up” does not fit because the time bits become infinitesimally small and end up becoming zero, and Zeno cannot stop the time from hitting infinity+1 parts, meaning that Achilles beats the tortoise.4) a) How did Archimedes console Conon’ friend Dositheus after Conon passed away?He sent him a proof to a new mathematical theorem.How awesome was this act? It was rude.b)Briefly describe what Archimedes did in the Quadrature of the Parabola.A parabola’s area is equal to 4/3 of triangle with the same sides.5) Do you think Archimedes had a modern understanding of infinity? ExplainNo.  He did not go to infinity, rather a real term N.  Our understanding of infinity is that it cannot be thought of as a number.