2) Suppose that Γ is a 4-paradoxical group and Γ = A1∪A2∪B1∪B2 is a paradoxical decomposition as defined above. Show that Γ plays ping-pong on itself, where the pingpong players are a := a−1 1 a2 and b := b −1 1 b2 .Deduce that Γ contains a non-abelian free subgroup F2. 3) Define the Tarski number T (Γ) of a group Γ to be the smallest integer N if it exists such that Γ is N -paradoxical. By the...

Most cases of fatal hypothermia are accidental, often in connection with alcoholisation, homelessness, age-related confusedness and others. The phenomenon of paradoxical undressing may be observed. A paradoxical feeling of warmth in the advanced condition of hypothermia leads to the behaviour of undressing, partly or completely. Suicides with intentional hypothermia are rare. Fatal hypothermia ...

in spite of the fact that paradox as an unknown literary device has largely been ignored, it has been a source of amazement and, consequently, aesthetic joy due to deviation from norm, ambiguity, the saliency of meaning, and laconism. one of the subtle points receiving little attention in arabic literature, especially in nahjol balaghah, is the study of paradoxical elements. the most significan...

To the Editor: The echocardiogram on the cover of the June 1, 1999, issue of Circulation is a beautiful illustration of an impending paradoxical embolism. Unfortunately, neither the text1 nor the key words of the article made any mention of this condition. Impending paradoxical embolism2 is a surgical emergency. This diagnosis would not have been possible before the advent of echocardiography. ...