Nyquist Frequency Confusion
For the number of samples given, your initial statement is false.  Sampling at exactly T/2 is a mathematical limit.  

For any finite number of samples, you need to sample a band-limited pure sinusoid of period T more frequently than T/2 to avoid aliasing or other pathologies, or at greater than 2X the highest spectrum frequency (for a baseband range). (and in real-life, to take into account the transition bandwidth and stop-band of any low-pass anti-aliasing filtering).  The shorter the sampling interval, the higher the sample rate needs to be above 2*Fmax (for a given baseband band-limited range) to reduce numerical, quantization, and other signal-to-noise induced errors to below some given threshold.

As you approach an infinite number of samples (beyond the life of the universe), you approach being able to reconstruct a sinewave with sampling at T/2.