With an average annual rate of 0.005 mm of erosion at the surface of the earth for the past four plus billion years, we can be confident in saying mountains still exist because:

Dynamics of the crust continue to produce mountains as the earth is cooling itself off That rate of weathering is not fast enough to have worn down the earth's original mountains 

Fluids passing through pores in the earth force the land up faster than erosion can break it down 

An internal heat engine (metaphor used by James Hutton) drives the vertical movements of crust to form continents and mountains

None of the above

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