Difference between revisions of "Proof by induction"
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| − | A much loved [[Further Maths]] topic, taught by [[Mr Reeves]], this is a form of mathematical proof, whereby a statement is proved true for all natural values of n. | + | A much loved [[Further Maths]] topic, this year taught by [[Mr Reeves]], this is a form of mathematical proof, whereby a statement is proved true for all natural values of n. |
It is decribed with an analogy of a ladder: If a ladder continues to infinity, can you say that you can climb to the top? If you can get on the first rung of the ladder, and then prove that you can move from one rung to the next at a general point on the ladder, then you can prove that you can climb it to the top. | It is decribed with an analogy of a ladder: If a ladder continues to infinity, can you say that you can climb to the top? If you can get on the first rung of the ladder, and then prove that you can move from one rung to the next at a general point on the ladder, then you can prove that you can climb it to the top. | ||
| − | ==An Example | + | =Cult following= |
| + | Having been taught proof by induction by [[Mrs Chapman]], the 2005-2007 Further Maths set pledged their allegiance to this noble form of proof. Subsequently, they have endeavoured to promote it to the 2006-2008 set; the pinnacle of the campaign being Tom Hyatt writing 'PROOF BY INDUCTION' on an interactive whiteboard. In dry-wipe marker. | ||
| + | |||
| + | =An Example= | ||
[[Image:Proofbyinduction.jpg]] | [[Image:Proofbyinduction.jpg]] | ||
Latest revision as of 16:49, 24 November 2010
A much loved Further Maths topic, this year taught by Mr Reeves, this is a form of mathematical proof, whereby a statement is proved true for all natural values of n.
It is decribed with an analogy of a ladder: If a ladder continues to infinity, can you say that you can climb to the top? If you can get on the first rung of the ladder, and then prove that you can move from one rung to the next at a general point on the ladder, then you can prove that you can climb it to the top.
Cult following
Having been taught proof by induction by Mrs Chapman, the 2005-2007 Further Maths set pledged their allegiance to this noble form of proof. Subsequently, they have endeavoured to promote it to the 2006-2008 set; the pinnacle of the campaign being Tom Hyatt writing 'PROOF BY INDUCTION' on an interactive whiteboard. In dry-wipe marker.
