If Six Integers Are Chosen from the Set {1, 2

question 21

Essay

If six integers are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, must there be at least two integers with the property that the sum of the smaller plus the larger is 11? Why or why not?
Write an answer that would convince a good but skeptical fellow student who has learned the statement of the pigeonhole principle but not seen an application like this one. Either describe the pigeons, the pigeonholes, and how the pigeons get to the pigeonholes, or describe a function by giving its domain, co-domain, and how elements of the domain are related to elements of the co-domain.

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Definitions:

Pruning

In neuroscience, the process by which extra neurons and synaptic connections are eliminated in the brain to increase the efficiency of neuronal transmissions.

Recommended Position

A stance or viewpoint endorsed by an authority or expert, typically based on evidence or consensus in a specific field.

Neural Connections

the links between neurons in the brain that enable communication through neurotransmitters, forming the basis for all brain functions, including thought and emotion.

Pruning Process

Neural pruning is the process by which extra neurons and synaptic connections are eliminated to increase the efficiency of neuronal transmissions.