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The Order (N) Tight Binding Molecular Dynamics (TBMD) algorithms applied to simulate the tensile elongations of short (2-2.5 nm) armchair and zigzag Single Walled Carbon Nanotubes (SWCNTs) without bond breakings or defect formation. Simulations are repeated at high temperatures. We fix the lower limit of breaking strains to short SWCNTs without bond breaking or 5-7 defects formation. At room temperature, the simulated (4,4) SWCNT is able to carry the strain up to 130% of the relaxed tube length without bond breaking or 5-7 defects formation. This value is 127% for (11,0) SWCNT, 125%for (17,0) SWCNT, 123% for (10,10) SWCNT. Bond breakings occur at lower strain values in defectfree, short nanotubes as the radii of the nanotubes increase, regardless of their chirality. This is true even when we heat the tubes to higher temperatures. Bond breaking strain values, tensile strength, Young's moduli of the SWCNTs are obtained as functions of temperature. In general, defect-free zigzag nanotubes exhibit higher tensile strength than armchaired ones. Young's moduli of defect-free individual single-wall nanotubes are found to be in the range of 0.400 TPa within the elastic limit. At room temperature and experimentally realizable strain values, thinner tubes are more resistant to bond breaking and zigzag tubes over armchair ones. The same trend still holds at high temperatures although the resistance to strain gets lowered. We observe a slight decrease of the tensile strength with increasing temperatures. A similar behavior is also observed in Young's moduli. These results are important in determining the true breaking strains of SWCNTs.