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When they say they've paid in, it doesn't exist: it is just a mathematical fact - that's not a nefarious thing, the system was not designed for this ageing population that we have, the demographic change that we now have.
It is a stubborn mathematical fact that the top fifth of the income distribution can accommodate only 20 percent of the population.
Or, as Professor Goodstein wryly put it: "It is a simple mathematical fact that if scientists keep multiplying faster than people, there will soon be more scientists than there are people". Or literary critics.
I realise it is part of my civic duty to vote, and yet, in my neighbourhood in New York I know for a mathematical fact that my vote doesn't matter.
The mathematical fact that the structure of a relativistic spacetime is almost fully determined by its causal structure alone16,17,18 motivates the causal set approach to quantum gravity19.
It is a mathematical fact that there is no particular rate of decay associated with each level of EH.
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The cold, hard mathematical fact is that, based on that conservative 10percentt rule of thumb, there are at least 10 times as many worthwhile shows around than there used to be.
Because no matter how many live speeches the candidates give -- no matter how many pancake breakfasts they attend or how many high-priced fundraisers they address -- the simple mathematical fact is that the overwhelming majority of voters will never get to hear a single candidate speak.
That's a mathematical fact".
That is a mathematical fact.
What is a mathematical fact, he says, is that if there are five models out there, or five ways of thinking of a problem, and you've only picked one, you're not going to do as well as if you pick all five.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com