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Small Steps
Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
Age 16 to 18 Challenge Level:
The symbol [ ] means 'the integer part of '.
Consider the three numbers
$$[2x];\ 2[x];\ [x + {1\over 2}] + [x - {1\over 2}]$$
Can they ever be equal?
Can they ever take three different values?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.