Sentence examples for thus without from inspiring English sources

Thus, without replenishment, any radioactive isotope will ultimately vanish.

Thus, without establishing a junta, the military strengthened its control of Argentina.

Thus, without structural reforms, the euro's economic promise may be wasted.

To pass the bill in the Senate with just fifty votes and thus without any Democratic support it also couldn't add more than $1.5 trillion to the deficit.

Since my husband had retired a few years earlier, we found ourselves without an employer and thus without health insurance.

Thus without loss of generality, we assume that (Aneqtheta).

Thus, without loss of generality, we assume γRD≥ΓR.

Thus without loss of generality, one can suppose that (Bneqtheta).

Thus, without power, technology cannot be adopted for production.

Thus, without confinement, good levels of performance can be achieved without precise spatial representations.

Thus, without loss of generality, it is sufficient to consider unary functions.