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Broad Topics > Advanced Algebra > Step functions

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Small Steps

Age 16 to 18 Challenge Level:

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.

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Eyes Down

Age 16 to 18 Challenge Level:

The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?